Skip to main content

Full text of "A budget of paradoxes. Reprinted, with the author's additions, from the 'Athenaeum"

See other formats


BUDGET    OF    PAEADOXES. 


LONDOM  :     PRINTED     BY 

SPOTTISWOODE    AND    CO.,    STEW-STREET    iQtJAEH 
A.VU    PARLIAMENT     fcTUKKT 


BUDGET    OF    PARADOXES, 


BT 


AUGUSTUS    DE    MORGAN, 

F.R.A.S.  &  C.P.S. 

OF  TRINITY  COLLEGE,  CAMB1UDGB. 


[REPRINTED,    WITH    THE    AUTHOR'S    ADDITIONS,    FROM    THE    ' 


'  Ut  agendo  snrgamus  arguendo  gustamus.' 
PTOCHODOKIAKCHUS 


LONDON : 
LONGMANS,    GREEN,    AND    CO. 

1872. 


A/I    rujhtt    referred. 


AC 


EDITOR'S    PREFACE. 


IT  is  not  without  hesitation  that  I  have  taken  upon  myself 
the  editorship  of  a  work  left  avowedly  imperfect  by  the 
author,  and,  from  its  miscellaneous  and  discursive  character, 
difficult  of  completion  with  due  regard  to  editorial  limita- 
tions by  a  less  able  hand. 

Had  the  author  lived  to  carry  out  his  purpose  he  would 
have  looked  through  his  Budget  again,  amplifying  and 
probably  rearranging  some  of  its  contents.  He  had  collected 
materials  for  further  illustration  of  Paradox  of  the  kind 
treated  of  in  this  book  ;  and  he  meant  to  write  a  second 
part,  in  which  the  contradictions  and  inconsistencies  of 
orthodox  learning  would  have  been  subjected  to  the  same 
scrutiny  and  castigation  as  heterodox  ignorance  had  already 
received. 

It  will  be  seen  that  the  present  volume  contains  more 
than  the  Athenaeum  Budget.  Some  of  the  additions  formed 
a  Supplement  to  the  original  articles.  These  supplementary 
paragraphs  were,  by  the  author,  placed  after  those  to  which 
they  respectively  referred,  being  distinguished  from  the  rest 
of  the  text  by  brackets.  I  have  omitted  these  brackets  as 
useless,  except  where  they  were  needed  to  indicate  sub- 
sequent writing. 


Vl  EDITOR'S    PREFACE. 

Another  and  a  larger  portion  of  the  work  consists  of 
discussion  of  matters  of  contemporary  interest,  for  the 
Budget  was  in  some  degree  a  receptacle  for  the  author's 
thoughts  on  any  literary,  scientific,  or  social  question. 
Having  grown  thus  gradually  to  its  present  size,  the  book 
as  it  was  left  was  not  quite  in  a  fit  condition  for  publication, 
but  the  alterations  which  have  been  made  are  slight  and 
few,  being  in  most  cases  verbal  and  such  as  the  sense 
absolutely  required,  or  transpositions  of  sentences  to  secure 
coherence  with  the  rest,  in  places  where  the  author,  in  his 
more  recent  insertion  of  them,  had  overlooked  the  connexion 
in  which  they  stood.  In  no  case  has  the  meaning  been  in 
any  degree  modified  or  interfered  with. 

One  rather  large  omission  must  be  mentioned  here.  It 
is  an  account  of  the  quarrel  between  Sir  James  South  and 
Mr.  Troughton  on  the  mounting,  &c.  of  the  equatorial 
telescope  at  Campden  Hill.  At  some  future  time  when  the 
affair  has  passed  entirely  out  of  the  memory  of  living 
Astronomers,  the  appreciative  sketch,  which  is  omitted  in 
this  edition  of  the  Budget,  will  be  an  interesting  piece  of 
history  and  study  of  character. 

A  very  small  portion  of  Mr.  James  Smith's  circle-squaring 
has  been  left  out,  with  a  still  smaller  portion  of  Mr.  De 
Morgan's  answers  to  that  Cyclometrical  Paradoxer. 

In  more  than  one  place  repetitions,  which  would  have 
disappeared  under  the  author's  revision,  have  been  allowed 
to  remain,  because  they  could  not  have  been  taken  away 
without  leaving  a  hiatus,  not  easy  to  fill  up  without  damage 
to  the  author's  meaning. 


EDITOR'S    PREFACE.  vii 

I  give  these  explanations  in  obedience  to  the  rules  laid 
down  for  the  guidance  of  editors  at  page  11.  If  any  apology 
for  the  fragmentary  character  of  the  book  be  thought 
necessary,  it  may  be  found  in  the  author's  own  words 
at  page  438. 

The  publication  of  the  Budget  could  not  have  been 
delayed  without  lessening  the  interest  attaching  to  the 
writer's  thoughts  upon  questions  of  our  own  day.  I  trust 
that,  incomplete  as  the  work  is  compared  with  what  it 
might  have  been,  I  shall  not  be  held  mistaken  in  giving  it 
to  the  world.  Bather  let  me  hope  that  it  will  be  welcomed 
as  an  old  friend  returning  under  great  disadvantages,  but 
bringing  a  pleasant  remembrance  of  the  amusement  which 
its  weekly  appearance  in  the  Athenceum  gave  to  both  writer 
and  reader. 

The  Paradoxes  are  dealt  with  in  chronological  order. 
This  will  be  a  guide  to  the  reader,  and  with  the  alphabetical 
Index  of  Names,  &c.,  will,  I  trust,  obviate  all  difficulty  of 
reference. 

SOPHIA  DE  MORGAN. 

6  MERTON  ROID,   PRIMROSE  HILL. 


Erratum. 
Page  40,  line  27,  for  Litchfield  read  Liehfield. 


A   BUDGET 

OP 


PARADOXES 


INTKODUCTOKY. 

IF  I  had  before  me  a  fly  and  an  elephant,  having  rever  seen 
more  than  one  such  magnitude  of  either  kind ;  and  if  the  fly 
were  to  endeavour  to  persuade  me  that  he  was  larger  than  the 
elephan^  I  might  by  possibility  be  placed  in  a  difficulty.  The 
apparently  little  creature  might  use  such  arguments  about  the 
effect  of  distance,  and  might  appeal  to  such  laws  of  sight  and 
hearing  as  I,  if  unlearned  in  those  things,  might  be  unable 
wholly  to  reject.  But  if  there  were  a  thousand  flies,  all  buzzing, 
to  appearance,  about  the  great  creature ;  and,  to  a  fly,  declaring, 
each  one  for  himself,  that  he  was  bigger  than  the  quadruped ; 
and  all  giving  different  and  frequently  contradictory  reasons  ;  and 
each  one  despising  and  opposing  the  reasons  of  the  others — I 
should  feel  quite  at  my  ease.  I  should  certainly  say,  My  little 
friends,  the  case  of  each  one  of  you  is  destroyed  by  the  rest.  I 
intend  to  show  flies  in  the  swarm,  with  a  few  larger  animals,  for 
reasons  to  be  given. 

In  every  age  of  the  world  there  has  been  an  established  system, 
which  has  been  opposed  from  time  to  time  by  isolated  and  dis- 
sentient reformers.  The  established -system  has  sometimes  fallen, 
slowly  and  gradually :  it  has  either  been  upset  by  the  rising  in- 
fluence of  some  one  man,  or  it  has  been  sapped  by  gradual  change 
of  opinion  in  the  many. 

I  have  insisted  on  the  isolated  character  of  the  dissentients,  as 
an  element  of  the  a  priori  probabilities  of  the  case.  Show  me  a 
schism,  especially  a  growing  schism,  and  it  is  another  thing.  The 
homceopathists,  for  instance,  shall  be,  if  any  one  so  think,  as 


2  A  BUDGET   OF  PARADOXES. 

wrong  as  St.  John  Long ;  but  an  organised  opposition,  supported 
by  the  efforts  of  many  acting  in  concert,  appealing  to  common 
arguments  and  experience,  with  perpetual  succession  and  a  com- 
•mon  seal,  as  the  Queen  says  in  the  charter,  is,  be  the  merit  of  the 
schism  what  it  may,  a  thing  wholly  different  from  the  case  of  the 
isolated  opponent  in  the  mode  of  opposition  to  it  which  reason 
points  out. 

During  the  last  two  centuries  and  a  half,  physical  knowledge 
has  been  gradually  made  to  rest  upon  a  basis  which  it  had  not 
before.  It  has  become  mathematical.  The  question  now  is,  not 
whether  this  or  that  hypothesis  is  better  or  worse  to  the  pure 
thought,  but  whether  it  accords  with  observed  phenomena  in 
those  consequences  which  can  be  shown  necessarily  to  follow  from 
it,  if  it  be  true.  Even  in  those  sciences  which  are  not  yet  under 
the  dominion  of  mathematics,  and  perhaps  never  will  be,  a 
working  copy  of  the  mathematical  process  has  been  made.  This 
is  not  known  to  the  followers  of  those  sciences  who  are  not  them- 
selves mathematicians,  and  who  very  often  exalt  their  horns  against 
the  mathematics  in  consequence.  They  might  as  well  be  squaring 
the  circle,  for  any  sense  they  show  in  this  particular. 

A  great  many  individuals,  ever  since  the  rise  of  the  mathematical 
method,  have,  each  for  himself,  attacked  its  direct  and  indirect 
consequences.  I  shall  not  here  stop  to  point  out  how  the  very 
accuracy  of  exact  science  gives  better  aim  than  the  preceding 
state  of  things  could  give.  I  shall  call  each  of  these  persons  a 
paradoxer,  and  his  system  a  paradox.  I  use  the  word  in  the  old 
sense :  a  paradox  is  something  which  is  apart  from  general 
opinion,  either  in  subject-matter,  method,  or  conclusion. 

Many  of  the  things  brought  forward  would  now  be  called 
crotchets,  which  is  the  nearest  word  we  have  to  old  paradox.  But 
there  is  this  difference,  that  by  calling  a  thing  a  crotchet  we  mean 
to  speak  lightly  of  it ;  which  was  not  the  necessary  sense  of  para- 
dox. Thus  in  the  sixteenth  century  many  spoke  of  the  earth's 
motion  as  the  paradox  of  Copernicus,  who  held  the  ingenuity  of 
that  theory  in  very  high  esteem,  and  some,  I  think,  who  even  in- 
clined towards  it.  In  the  seventeenth  century,  the  depravation 
of  meaning  took  place,  in  England  at  least.  Phillips  says  paradox 
is  '  a  thing  which  seemeth  strange  ' — here  is  the  old  meaning : 
after  a  colon,  he  proceeds — '  and  absurd,  and  is  contrary  to  common 
opinion,'  which  is  an  addition  due  to  his  own  time. 

Some  of  my  readers  are  hardly  inclined  to  think  that  the  word 
paradox  could  once  have  had  no  disparagement  in  its  meaning  ; 
still  less  that  persons  could  have  applied  it  to  themselves.  I 


INTRODUCTORY.  3 

chance  to  have  met  with  a  case  in  point  against  them.  It  is 
Spinoza's  '  Pbilosophia  ScripturaB  Interpres,  Exercitatio  Paradoxa,' 
printed  anonymously  at  Eleutheropolis,  in  1666.  This  place 
was  one  of  several  cities  in  the  clouds,  to  which  the  cuckoos  re- 
sorted who  were  driven  away  by  the  other  birds  ;  that  is,  a  feigned 
place  of  printing,  adopted  by  those  who  would  have  caught  it  if 
orthodoxy  could  have  caught  them.  Thus,  in  1656,  the  works  of 
Socinus  could  only  be  printed  at  Irenopolis.  The  author  deserves 
his  self-imposed  title,  as  in  the  following : — 

Quanto  sane  satius  fuissefc  illam  [Trinitatem]  pro  mysterio  non 
habuisse,  et  Philosophiae  ope,  antequam  quod  esset  statuerent,  secun- 
dum  verse  logices  praecepta  quid  esset  cum  Cl.  Keckermanno  inves- 
tigasse ;  tanto  fervore  ac  labore  in  profundissimas  speluncas  et 
obscurissimos  metaphysicarum  speculationum  atque  fictionum  recessus 
se  recipere  ut  ab  adversariorum.  telis  sententiam  suam  in  tuto  collo- 
carent.  Profecto  magnus  ille  vir  .  .  .  dogma  illud,  quamvis  apud 
theologos  eo  nomine  non  multum  gratiee  iniverit,  ita  ex  immotis 
Philosophies  fundamentis  explicat  ac  demonstrat,  ut  paucis  tantum 
immutatis,  atque  additis,  nihil  amplius  animus  veritate  sincere  deditus 
desiderare  possit. 

This  is  properly  paradox,  though  also  heterodox.  It  supposes, 
contrary  to  all  opinion,  orthodox  and  heterodox,  that  philosophy 
can,  with  slight  changes,  explain  the  Athanasiau  doctrine  so  as  to 
be  at -least  compatible  with  orthodoxy.  The  author  would  stand 
almost  alone,  if  not  quite  ;  and  this  is  what  he  meant.  I  have 
met  with  the  counter-paradox.  I  have  heard  it  maintained  that 
the  doctrine  as  it  stands,  in  all  its  mystery,  is  a  priori  more 
likely  than  any  other  to  have  been  Revelation,  if  such  a  thing 
were  to  be  ;  and  that  it  might  almost  have  been  predicted. 

After  looking  into  books  of  paradoxes  for  more  than  thirty 
years,  and  holding  conversation  with  many  persons  who  have 
written  them,  and  many  who  might  have  done  so,  there  is  one 
point  on  which  my  mind  is  fully  made  up.  The  manner  in 
which  a  paradoxer  will  show  himself,  as  to  sense  or  nonsense,  will 
not  depend  upon  what  he  maintains,  but  upon  whether  he  has  or 
lias  not  made  a  sufficient  knowledge  of  what  has  been  done  by 
others,  especially  as  to  the  mode  of  doing  it,  a  preliminary  to  in-, 
venting  knowledge  for  himself.  That  a  little  knowledge  is  a 
dangerous  thing  is  one  of  the  most  fallacious  of  proverbs.  A 
person  of  small  knowledge  is  in  danger  of  trying  to  make  his 
little  do  the  work  of  more  ;  but  a  person  without  any  is  in  more 
danger  of  making  his  no  knowledge  do  the  work  of  some.  .  Take 
the  speculations  on  the  tides  as  an  instance.  Persons  with  nothing 

"  2 


4  A   BUDGET  OF  PAKADOXES. 

but  a  little  geometry  have  certainly  exposed  themselves  in  their 
modes  of  objecting  to  results  which  require  the  higher  mathe- 
matics to  be  known  before  an  independent  opinion  can  be  formed 
on  sufficient  grounds.  But  persons  with  no  geometry  at  all  have 
done  the  same  thing  much  more  completely. 

There  is  a  line  to  be  drawn  which  is  constantly  put  aside  in  the 
arguments  held  by  parodoxers  in  favour  of  their  right  to  instruct 
the  world.  Most  persons  must,  or  at  least  will,  like  the  lady  in 
Cadogan  Place,1  form  and  express  an  immense  variety  of  opinions 
on  an  immense  variety  of  subjects ;  and  all  persons  must  be  their 
own  guides  in  many  things.  So  far  all  is  well.  But  there  are 
many  who,  in  carrying  the  expression  of  their  own  opinions  beyond 
the  usual  tone  of  private  conversation,  whether  they  go  no  fur- 
ther than  attempts  at  oral  proselytism,  or  whether  they  commit 
themselves  to  the  press,  do  not  reflect  that  they  have  ceased  to 
stand  upon  the  ground  on  which  their  process  is  defensible.  As- 
piring to  lead  others,  they  have  never  given  themselves  the  fair 
chance  of  being  first  led  by  other  others  into  something  better 
than  they  can  start  for  themselves ;  and  that  they  should  first 
do  this  is  what  both  those  classes  of  others  have  a  fair  right  to 
expect.  New  knowledge,  when  to  any  purpose,  must  come  by 
contemplation  of  old  knowledge,  in  every  matter  which  concerns 
thought ;  mechanical  contrivance  sometimes,  not  very  often, 
escapes  this  rule.  All  the  men  who  are  now  called  discoverers,  in 
every  matter  ruled  by  thought,  have  been  men  versed  in  the  minds 
of  their  predecessors,  and  learned  in  what  had  been  before  them. 
There  is  not  one  exception.  I  do  not  say  that  every  man  has 
made  direct  acquaintance  with  the  whole  of  his  mental  ancestry  ; 
many  have,  as  I  may  say,  only  known  their  grandfathers  by  the 
report  of  their  fathers.  But  even  on  ;this  point  it  is  remarkable 
how  many  of  the  greatest  names  in  all  departments  of  knowledge 
have  been  real  antiquaries  in  their  several  subjects.  ., 

I  may  cite,  among  those  who  have  wrought  strongly  upon 
opinion  or  practice  in  science,  Aristotle,  Plato,  Ptolemy,  Euclid, 
Archimedes,  Eoger  Bacon,  Copernicus,  Francis  Bacon,  Ramus, 
Tycho  Brahe,  Galileo,  Napier,  Descartes,  Leibnitz,  Newton, 
Locke.  I  take  none  but  names  known  out  of  their  fields  of  work ; 
and  all  were  learned  as  well  as  sagacious.  I  have  chosen  my 
instances  :  if  any  one  will  undertake  to  show  a  person  of  little  or 
no  knowledge  who  has  established  himself  in  a  great  matter  ot 
pure  thought,  let  him  bring  forward  his  man,  and  we  shall  see. 

This  is  the  true  way  of  putting  off  those  who    plague  others 

1  Mrs.  Wititterly,  in  Nicholas  Nickleby. 


INTRODUCTORY.  5 

with  their  great  discoveries.  The  first  demand  made  should  be 
— Mr.  Moses,  before  I  allow  you  to  lead  me  over  the  Eed  Sea,  I 
must  have  you  show  that  you  are  learned  in  all  the  wisdom  of  the 
Egyptians  upon  your  own  subject.  The  plea  that  it  is  unlikely 
that  this  or  that  unknown  person  should  succeed  where  Newton, 
&c.  have  failed,  or  should  show  Newton,  &c.  to  be  wrong,  is  utterly 
null  and  void.  It  was  worthily  versified  by  Sylvanus  Morgan 
(the  great  herald  who  in  his  '  Sphere  of  Gentry '  gave  coat  armour 
to  '  Gentleman  Jesus,'  as  he  said),  who  sang  of  Copernicus  as 
follows  (1652):— 

If  Tellus  winged  be, 
The  earth  a  motion  round  ; 
Then  much  deceived  are  they 
Who  nere  before  it  found. 
Solomon  was  the  wisest, 
His  wit  nere  this  attained ; 
Cease,  then,  Copernicus, 
Thy  hypothesis  vain. 

Newton,  &c.  were  once  unknown  ;  but  they  made  themselves 
known  by  what  they  knew,  and  then  brought  forward  what  they 
could  do ;  which  I  see  is  as  good  verse  as  that  of  Herald  Sylvanus. 
The  demand  for  previous  knowledge  disposes  of  twenty-nine  cases 
out  of  thirty,  and  the  thirtieth  is  worth  listening  to. 

I  have  not  set  down  Copernicus,  Galileo,  &c.  among  the  para- 
doxers,  merely  because  everybody  knows  them ;  if  my  list  were 
quite  complete,  they  would  have  been  in  it.  But  the  reader  will 
find  Gilbert,  the  great  precursor  of  sound  magnetical  theory ;  and 
several  others  on  whom  no  censure  can  be  cast,  though  some  of 
their  paradoxes  are  inadmissible,  some  unproved,  and  some  capital 
jokes,  true  or  false  :  the  author  of  the  'Vestiges  of  Creation'  is  an 
instance.  I  expect  that  my  old  correspondent,  General  Perronet 
Thompson,  will  admit  that  his  geometry  is  part  and  parcel  of  my 
plan  ;  and  also  that,  if  that  plan  embraced  politics,  he  would 
claim  a  place  for  his  '  Catechism  on  the  Corn  Laws,'  a  work  at  one 
time  paradoxical,  but  which  had  more  to  do  with  the  abolition  of 
the  bread-tax  than  Sir  Robert  Peel. 

My  intention  in  publishing  this  Budget  in  the  Athenceum  is 
to  enable  those  who  have  been  puzzled  by  one  or  two  discoverers 
to  see  hoiv  they  look  in  the  lump.  The  only  question  is,  has  the 
selection  been  fairly  made  ?  To  this  my  answer  is,  that  no  selec- 
tion at  all  has  been  made.  The  books  are,  without  exception, 
those  which  I  have  in  my  own  library  ;  and  I  have  taken  all — I 
mean  all  of  the  kind :  Heaven  forbid  that  I  should  be  supposed 


6  A  BUDGET   OF  PARADOXES. 

to  have  no  other  books  !  But  I  may  have  been  a  collector,  in- 
fluenced in  choice  by  bias  ?  I  answer  that  I  never  have  collected 
books  of  this  sort — that  is,  I  have  never  searched  for  them,  never 
made  up  my  mind  to  look  out  for  this  book  or  that.  I  have 
bought  what  happened  to  come  in  my  way  at  shop  or  auction  ;  I 
have  retained  what  came  in  as  part  of  the  undescribed  portion  of 
miscellaneous  auction  lots ;  I  have  received  a  few  from  friends 
who  found  them  among  what  they  called  their  rubbish ;  and  I 
have  preserved  books  sent  to  me  for  review.  In  not  a  few  in- 
stances the  books  have  been  bound  up  with  others,  unmentioned 
at  the  back ;  and  for  years  I  knew  no  more  I  had  them  than  I 
knew  I  had  Lord  Macclesfield's  speech  on  moving  the  change  of 
Style,  which,  after  I  had  searched  shops,  &c.  for  it  in  vain,  I 
found  had  been  reposing  on  my  own  shelves  for  many  years,  at 
the  end  of  a  summary  of  Leibnitz's  philosophy.  Consequently,  I 
may  positively  affirm  that  the  following  list  is  formed  by  accident 
and  circumstance  alone,  and  that  it  truly  represents  the  casualties 
of  about  a  third  of  a  century.  For  instance,  the  large  proportion 
of  works  on  the  quadrature  of  the  circle  is  not  my  doing  :  it  is 
the  natural  share  of  this  subject  in  the  actual  run  of  events. 

[I  keep  to  my  plan  of  inserting  only  such  books  as  I  possessed 
in  1863,  except  by  casual  notice  in  aid  of  my  remarks.  I  have 
found  several  books  on  my  shelves  which  ought  to  have  been 
inserted.  These  have  their  titles  set  out  at  the  commencement 
of  their  articles,  in  leading  paragraphs  ;  the  casuals  are  without 
this  formality.1] 

Before  proceeding  to  open  the  Budget,  I  say  something  on  niy 
personal  knowledge  of  the  class  of  discoverers  who  square  the 
circle,  upset  Newton,  &c.  I  suspect  I  know  more  of  the  English 
class  than  any  man  in  Britain.  I  never  kept  any  reckoning ;  but 
I  know  that  one  year  with  another — and  less  of  late  years  than  in 
earlier  time — I  have  talked  to  more  than  rive  in  each  year,  giving 
more  than  a  hundred  and  fifty  specimens.  Of  this  I  am  sure, 
that  it  is  my  own  fault  if  they  have  not  been  a  thousand.  Nobody 
knows  how  they  swarm,  except  those  to  whom  they  naturally 
resort.  They  are  in  all  ranks  and  occupations,  of  all  ages  and 
characters.  They  are  very  earnest  people,  and  their  purpose  is 
bonafide  the  dissemination  of  their  paradoxes.  A  great  many — 
the  mass,  indeed — are  illiterate,  and  a  great  many  waste  their 
means,  and  are  in  or  approaching  penury.  But  I  must  say  that 
never,  in  any  one  instance,  has  the  quadrature  of  the  circle,  of 

1  The   brackets  mean  that  the  paragraph   is  substantially  from  some  one  of  the 
Athenceitm  Supplements. — (En.) 


INTRODUCTORY.  7 

the  like,  been  made  a  pretext  for  begging ;  even  to  be  asked  to 
purchase  a  book  is  of  the  very  rarest  occurrence — it  has  happened, 
and  that  is  all. 

These  discoverers  despise  one  another :  if  there  were  the  concert 
among  them  which  there  is  among  foreign  mendicants,  a  man 
who  admitted  one  to  a  conference  would  be  plagued  to  death.  I 
once  gave  something  to  a  very  genteel  French  applicant,  who 
overtook  me  in  the  street,  at  my  own  door,  saying  he  had  picked 
up  my  handkerchief :  whether  he  picked  it  up  in  my  pocket  for 
an  introduction,  I  know  not.  But  that  day  week  came  another 
Frenchman  to  my  house,  and  that  day  fortnight  a  French  lady ; 
both  failed,  and  I  had  no  more  trouble.  The  same  thing  hap- 
pened with  Poles.  It  is  not  so  with  circle-squarers,  &c. :  they 
know  nothing  of  each  other.  Some  will  read  this  list,  and  will 
say  I  am  right  enough,  generally  speaking,  but  that  there  is  an 
"  exception,  if  I  could  but  see  it. 

I  do  not  mean,  by  my  confession  of  the  manner  in  which  I 
have  sinned  against  the  twenty-four  hours,  to  hold  myself  out  as 
accessible  to  personal  explanation  of  new  plans.  Quite  the  con- 
trary :  I  consider  myself  as  having  made  my  report,  and  being 
discharged  from  further  attendance  on  the  subject.  I  will  not, 
from  henceforward,  talk  to  any  squarer  of  the  circle,  trisector  of 
the  angle,  duplicator  of  the  cube,  constructor  of  perpetual  motion, 
subverter  of  gravitation,  stagnator  of  the  earth,  builder  of  the 
universe,  &c.  I  will  receive  any  writings  or  books  which  require 
no  answer,  and  read  them  when  I  please  :  I  will  certainly  preserve 
them — this  list  may  be  enlarged  at  some  future  time. 

There  are  three  subjects  which  I  have  hardly  anything  upon; 
astrology,  mechanism,  and  the  infallible  way  of  winning  at  play. 
I  have  never  cared  to  preserve  astrology.  The  mechanists  make 
models,  and  not  books.  The  infallible  winners — though  I  have 
seen  a  few — think  their  secret  too  valuable,  and  prefer  mutare 
qu<tdrata  rotundis — to  turn  dice  into  coin — at  the  gaming-house  : 
verily  they  have  their  reward. 

I  shall  now  select,  to  the  mystic  number  sev  jn,  instances  of  my 
personal  knowledge  of  those  who  think  they  have  discovered,  in 
illustration  of  as  many  misconceptions. 

1.  Attempt  by  help  of  the  old  philosophy,  the  discoverer  not 
being  in  possession  of  modern  knowledge.  A  poor  schoolmaster, 
in  rags,  introduced  himself  to  a  scientific  friend  with  whom  I  was 
talking,  and  announced  that  he  had  found  out  the  composition  of 
the  sun.  '  How  was  that  done  ?  ' — '  By  consideration  of  the  four 
elements.' — '  What  are  they  ?  ' — '  Of  course,  fire,  air,  earth,  and 


A   BUDGET   OF  PARADOXES. 


water  -'Did  you  not  know  that  air,  earth,  and  water,  have  Ion, 
been  known  to  be  no  elements  at  all,  but  compounds  V_<  Wh 
do  you  mean,  sir  ?     Who  ever  heard  of  such  a  thing  ?  '' 

2.  The  noUonthat  difficulties  are  enigmas,  to  be  overcome  in 
a  moment  by  a  lucky  thought.     A  nobleman  of  very  hET£fc 
now  long  dead,  read  an  article   by  me  on  the  quadrature  in 
early  number  of  the  Penny  Magazine.    He  had,  I  suppose  sc 
recollections  of  geometry.     He  put  pencil  to  paper,  dTw  a     rcle 
and  constructed  what  seemed  likely  to  answer,  and  indeed,  wa  - 
as  he  said-  certain,  if  only  this  bit  were  equal  to  that  ;  wiTh  of 
course  it  was  not      He  forwarded  his  diagram  to  the  Secreta  y 
the  Diffusion  Society,  to  be  handed  to  the  author  of  the  art  Lie 
case  the  difficulty  should  happen  to  be  therein  overcome 

3.  Discovery  at   all  hazards,  to  get  on  in  the  world.     Thirty 
years  ago,  an  officer  of  rank,  just  come  from  foreign  service  and 
trying  for  a  decoration  from  the  Crown,  found  that  his  claim  'were 
of  doubtful  amount  and  was  told  by  a  friend  that  so  and  To  who 

ttn^owt^6  ^  ^.f  df  °nal  Cklm  °f  S™°  «± 

but  that  if  some  clever  fellow  would   mi*  f»,o  *i  • 
light  he  thought  his  affair  m 


e      a  poper 


.    th      ,  '  > 

,  that  though  perhaps  they  were  wrong,  the  advisers 


^     H1S  r6SUIt  WaS  abou       ' 


He  came  to  In  7         ?        ^     H1S  r6SUIt  WaS  about 

ame  to  London,  and  somebody  sent  him  to  me.     Like  manv 

ht  min°d        PUrSUU'  h6  Seemed  t0  ha™  t"™*  «>«  whole  fo^  of 


LO  rfMiiriTirm          TT      l.      i  i  "WH.LU.   uc  UfJtJlJ. 


INTRODUCTORY.  9 

Memoirs,  in  which  were  a  large  number  of  observed  places  of  the 
planets  compared  with  prediction,  and  asked  him  whether  it  could 
be  possible  that  persons  who  did  not  know  the  circle  better  than 
he  had  found  it  could  make  the  calculations,  of  which  I  gave  him 
a  notion,  so  accurately  ?  He  was  perfectly  astonished,  and  took 
the  titles  of  some  books  which  he  said  he  would  read. 

5.  Application  for  the  reward  from  abroad.     Many  years  ago, 
about  twenty-eight,  I  think,  a  Jesuit  came  from  South  America, 
with  a  quadrature,  and  a  cutting  from  a  newspaper,  announcing 
that  a  reward  was  ready  for  the  discovery  in  England.     On  this 
evidence  he  came  over.     After  satisfying  him  that  nothing  had 
ever  been  offered  here,  I  discussed  his  quadrature,  which  was  of 
no  use.     I  succeeded  better  when  I  told  him  of  Richard  White, 
also  a  Jesuit,  and  author  of  a  quadrature  published  before  1648, 
under  the  name  of  Chryscespis,-of  which  I  can  give  no  account, 
having  never  seen  it.     This  White  (Albius)  is  the  only  quad- 
rator  who  was  ever  convinced  of  his  error.     My  Jesuit  was  struck 
by  the  instance,  and  promised  to  read  more  geometry — he  was 
no  Clavius — before  he  published  his  book.     He  relapsed,  how- 
ever, for  I  saw  his  book  advertised  in  a  few  days.     I  may  say,  as 
sufficient  proof  of  my  being  no  collector,  that  I  had  not  the 
curiosity  to  buy  this  book  ;  and  my  friend  the  Jesuit  did  not 
send  me  a  copy,  which  he  ought  to  have  done,  after  the  hour  I 
had  given  him. 

6.  Application  for   the   reward  at  home.       An   agricultural 
labourer  squared  the  circle,  and  brought  the  proceeds  to  London. 
He  left  his  papers  with  me,  one  of  which  was  the  copy  of  a  letter 
to   the   Lord   Chancellor,   desiring   his   Lordship  to  hand  over 
forthwith  100,000^.,  the  amount  of  the  alleged   offer  of  reward. 
He  did  not  go  quite  so  far  as  M.  de  Vausenville,  who,  I  think 
in  1778,  brought  an  action  against  the  Academy  of  Sciences  to 
recover  a  reward  to  which  he  held  himself  entitled.     I  returned 
the  papers,  with  a  note,  stating  that  he  had  not  the  knowledge 
requisite  to  see  in  what  the  problem  consisted.     I  got  for  answer 
a  letter  in  which  I  was  told  that  a  person  who  could  not  see  that 
he  had  done  the  thing  should  '  change   his  business,  and  appro- 
priate his  time  and  attention  to  a  Sunday-school,  to  learn  what 
he  could,  and  keep  the  litle  children  from   durting  their  close.' 
I  also  received  a  letter  from  a  friend  of  the  quadrator,  informing 
me  that  I  knew  his  friend  had  succeeded,  and  had  been  heard  to 
say  so.     These  letters  were  printed — without  the  names   of  the 
writers — for  the  amusement  of  the  readers  of  Notes  and  Queries, 
First  Series,  xii.  57,  and  they  will  appear  again  in  the  sequel. 


10  A   BUDGET   OF   PAKADOXES. 

[There  are  many  who  have  such  a  deep  respect  for  any  attempt 
at  thought  that  they  are  shocked  at  ridicule  even  of  those  who 
have  made  themselves  conspicuous  by  pretending  to  lead  the 
world  in  matters  which  they  have  not  studied.  Among  my 
anonymes  is  a  gentleman  who  is  angry  at  my  treatment  of 
the  '  poor  but  thoughtful '  man  who  is  described  in  my  intro- 
duction as  recommending  me  to  go  to  a  Sunday-school  because  I 
informed  him  that  he  did  not  know  in  what  the  difficulty  of 
quadrature  consisted.  My  impugner  quite  forgets  that  this 
man's  '  thoughtfulness '  chiefly  consisted  in  his  demanding  a 
hundred  thousand  pounds  from  the  Lord  Chancellor  for  his  dis- 
covery; and  I  may  add,  that  his  greatest  stretch  of  invention 
was  finding  out  that  '  the  clergy '  were  the  means  of  his  modest 
request  being  unnoticed.  I  mention  this  letter  because  it  affords 
occasion  to  note  a  very  common  error,  namely,  that  men  unread 
in  their  subjects  have,  by  natural  wisdom,  been  great  benefactors 
of  mankind.  My  critic  says,  '  Shakspeare,  whom  the  Pror  (sic) 
may  admit  to  be  a  wisish  man,  though  an  object  of  contempt  as 
to  learning.  .  .  .'  Shakspeare  an  object  of  contempt  as  to 
learning !  Though  not  myself  a  thoroughgoing  Shakspearean — 
and  adopting  the  first  half  of  the  opinion  given  by  George  III., 
'What!  is  there  not  sad  stuff?  only  one  must  not  say  so' — I 
am  strongly  of  opinion  that  he  throws  out  the  masonic  signs  of 
learning  in  almost  every  scene,  to  all  who  know  what  they  are. 
And  this  over  and  above  every  kind  of  direct  evidence.  First, 
foremost,  and  enough,  the  evidence  of  Ben  Jonson  that  he  had 
'little  Latin  and  less  Greek;'  then  Shakspeare  had  as  much 
Greek  as  Jonson  would  call  some,  even  when  he  was  depreciating. 
To  have  any  Greek  at  all  was  in  those  days  exceptional.  In 
Shakspeare's  youth  St.  Paul's  and  Merchant  Taylors'  schools  were 
to  have  masters  learned  in  good  and  clean  Latin  literature,  and 
also  in  Greek  if  such  may  be  gotten.  When  Jonson  spoke  as 
above,  he  intended  to  put  Shakspeare  low  among  the  learned, 
but  not  out  of  their  pale ;  and  he  spoke  as  a  rival  dramatist,  who 
was  proud  of  his  own  learned  sock ;  and  it  may  be  a  subject  of 
inquiry  how  much  Latin  he  would  call  little.  If  Shakspeare's 
learning  on  certain  points  be  very  much  less  visible  than  Jonson's, 
it  is  partly  because  Shakspeare's  writings  hold  it  in  chemical 
combination,  Jonson's  in  mechanical  aggregation.] 

7.  An  elderly  man  came  to  me,  to  show  me  how  the  universe 
was  created.  There  was  one  molecule,  which  by  vibration  became 
— Heaven  knows  how  ! — the  Sun.  Further  vibration  produced 
Mercury,  and  so  on.  I  suspect  the  nebular  hypothesis  had  got 


INTRODUCTORY.  1 1 

into  the  poor  man's  head  by  reading,  in  some  singular  mixture 
with  what  it  found  there.  Some  modifications  of  vibration  gave 
heat,  electricity,  &c.  I  listened  until  my  informant  ceased  to 
vibrate — which  is  always  the  shortest  way — and  then  said,  '  Our 
knowledge  of  elastic  fluids  is  imperfect.'  '  Sir  ! '  said  he,  '  I 
see  you  perceive  the  truth  of  what  I  have  said,  and  I  will 
reward  your  attention  by  telling  you  what  I  seldom  disclose, 
never,  except  to  those  who  can  receive  my  theory — the  little 
molecule  whose  vibrations  have  given  rise  to  our  solar  system  is 
the  Logos  of  St.  John's  Gospel ! '  He  went  away  to  Dr.  Lardner, 
who  would  not  go  into  the  solar  system  at  all — the  first  molecule 
settled  the  question.  So  hard  upon  poor  discoverers  are  men  of 
science  who  are  not  antiquaries  in  their  subject !  On  leaving, 
he  said,  '  Sir,  Mr.  De  Morgan  received  me  in  a  very  different 
way  ;  he  heard  me  attentively,  and  I  left  him  perfectly  satisfied 
of  the  truth  of  my  system.'  I  have  had  much  reason  to  think 
that  many  discoverers,  of  all  classes,  believe  they  have  convinced 
every  one  who  is  not  peremptory  to  the  verge  of  incivility. 

My  list  is  given  in  chronological  order.  My  readers  will 
understand  that  my  general  expressions,  where  slighting  or 
contemptuous,  refer  to  the  ignorant,  who  teach  before  they 
have  learnt.  In  every  instance,  those  of  whom  I  am  able  to 
speak  with  respect,  whether  as  right  or  wrong,  have  sought 
knowledge  in  the  subject  they  were  to  handle  before  they  com- 
pleted their  speculations.  I  shall  further  illustrate  this  at  the 
conclusion  of  my  list. 

Before  I  begin  the  list,  I  give  prominence  to  the  following 
letter,  addressed  by  me  to  the  Correspondent  of  October  28,  1865. 
Some  of  my  paradoxers  attribute  to  me  articles  in  this  or  that 
journal ;  and  others  may  think — I  know  some  do  think — they 
know  me  as  the  writer  of  reviews  of  some  of  the  very  books 
noticed  here.  The  following  remarks  will  explain  the  way  iu 
which  they  may  be  right,  and  in  whicli  they  may  be  wrong : — 

THE, EDITORIAL  SYSTEM. 

SIR, — I  have  reason  to  think  that  many  persons  Lave  a  very  in- 
accurate notion  of  the  Editorial  system.  What  1  call  by  this  name  has 
grown  up  in  the  last  centenary — a  word  I  may  use  to  signify  the 
hundred  years  now  ending,  arid  to  avoid  the  ambiguity  of  century.  It 
cannot  conveniently  be  explained  by  editors  themselves,  and  edited 
journals  generally  do  not  like  to  say  much  about  it.  In  your  paper 
parhaps,  in  which  editorial  duties  differ  somewhat  from  those  of 
ordinary  journals,  the  common  system  may  be  freely  spoken  of. 


12  A  BUDGET   OF  PARADOXES. 

When  a  reviewed  author,  as  very  often  happens,  writes  to  the 
editor  of  the  reviewing  journal  to  complain  of  what  has  been  said  of 
him,  he  frequently — even  more  often  than  not — complains  of  'your 
reviewer.'  He  sometimes  presumes  that  '  you '  have,  '  through 
inadvertence '  in  this  instance,  '  allowed  some  incompetent  person  to 
lower  the  character  of  your  usually  accurate  pages.'  Sometimes  he 
talks  of  'your  scribe,'  and,  in  extreme  cases,  even  of  '  your  hack.'  All 
this  shows  perfect  ignorance  of  the  journal  system,  except  where  it  is 
done  under  the  notion  of  letting  the  editor  down  easy.  But  the  editor 
never  accepts  the  mercy. 

All  that  is  in  a  journal,  except  what  is  marked  as  from  a  corre- 
spondent, either  by  the  editor  himself  or  by  the  correspondent's  real 
or  fictitious  signature,  is  published  entirely  on  editorial  responsibility, 
as  much  as  if  the  editor  had  written  it  himself.  The  editor,  therefore, 
may  claim,  and  does  claim  and  exercise,  unlimited  right  of  omission, 
addition,  and  alteration.  This  is  so  well  understood  that  the  editor 
performs  his  last  function  on  the  last  revise  without  the  '  contributor ' 
knowing  what  is  done.  The  word  contributor  is  the  proper  one :  it 
implies  that  he  furnishes  materials  without  stating  what  he  furnishes 
or  how  much  of  it  is  accepted,  or  whether  he  be  the  only  contributor. 
All  this  applies  both  to  political  and  literary  journals.  No  editor 
acknowledges  the  right  of  a  contributor  to  withdraw  an  article,  if  he 
should  find  alterations  in  the  proof  sent  to  him  for  correction  which 
would  make  him  wish  that  the  article  should  not  appear.  If  the 
demand  for  suppression  were  made — I  say  nothing  about  what  might 
be  granted  to  request — the  answer  would  be,  '  It  is  not  your  article, 
but  mine ;  I  have  all  the  responsibility ;  if  it  should  contain  a  libel,  I 
could  not  give  you  up,  even  at  your  own  desire.  You  have  furnished 
me  with  materials,  on  the  known  and  common  understanding  that  I 
was  to  use  them  at  my  discretion,  and  you  have  no  right  to  impede  my 
operations  by  making  the  appearance  of  the  article  depend  on  your 
approbation  of  my  use  of  your  materials.' 

There  is  something  to  be  said  for  this  system,  and  something  against 
it — I  mean  simply  on  its  own  merits.  But  the  all-conquering  argu- 
ment in  its  favour  is,  that  the  only  practicable  alternative  is  the 
modern  French  plan  of  no  articles  without  the  signature  of  the  writers. 
I  need  not  discuss  this  plan ;  there  is  no  collective  party  in  favour  of 
it.  Some  may  think  it  is  not  the  only  alternative  ;  they  have  not  pro- 
duced any  intermediate  proposal  in  which  any  dozen  of  persons  have 
concurred.  Many  will  say,  Is  not  all  this,  though  perfectly  correct, 
well  known  to  be  matter  of  form  ?  Is  it  not  practically  the  course  of 
events  that  an  engaged  contributor  writes  the  article,  and  sends  it  to 
the  editor,  who  admits  it  as  written — substantially,  at  least  ?  And  is 
it  not  often  very  well  known,  by  style  and  in  other  ways,  who  it  was 
wrote  the  article  ?  This  system  is  matter  of  form  just  as  much  as 
loaded  pistols  are  matter  of  form  so  long  as  the  wearer  is  not  assailed ; 
but  matter  of  form  takes  the  form  of  matter  in  the  pulling  of  a  trigger, 


INTRODUCTORY.  13 

so  soon  as  the  need  arises.  Editors  aud  contributors  who  can  work 
together  find  each  other  out  by  elective  affinity,  so  that  the  common 
run  of  events  settles  down  into  most  articles  appearing  much  as  they 
are  written.  And  there  are  two  safety-valves  ;  that  is,  when  judicious 
persons  come  together.  In  the  first  place,  the  editor  himself,  when  he 
has  selected  his  contributor,  feels  that  the  contributor  is  likely  to  know 
his  business  better  than  an  editor  can  teach  him  ;  in  fact,  it  is  on 
that  principle  that  the  selection  is  made.  But  he  feels  that  he  is  more 
competent  than  the  writer  to  judge  questions  of  strength  and  of  tone, 
especially  when  the  general  purpose  of  the  journal  is  considered,  of 
which  the  editor  is  the  judge  without  appeal.  An  editor  who  meddles 
with  substantive  matter  is  likely  to  be  wrong,  even  when  he  knows  the 
subject ;  but  one  who  prunes  what  he  deems  excess,  is  likely  to  be 
right,  even  when  he  does  not  know  the  subject.  In  the  second  place, 
a  contributor  knows  that  he  is  supplying  an  editor,  and  learns,  without 
suppressing  truth  or  suggesting  falsehood,  to  make  the  tone  of  his  com- 
munications suit  the  periodical  in  which  they  are  to  appear.  Hence 
it  very  often  arises  that  a  reviewed  author,  who  thinks  he  knows  the 
name  of  his  reviewer,  and  proclaims  it  with  expressions  of  dissatis- 
faction, is  only  wrong  in  supposing  that  his  critic  has  given  all  his 
mind.  It  has  happened  to  myself,  more  than  once,  to  be  announced  as 
the  author  of  articles  which  I  could  not  have  signed,  because  they  did 
not  go  far  enough  to  warrant  my  affixing  my  name  to  them  as  to  a 
sufficient  expression  of  my  own  opinion. 

There  are  two  other  ways  in  which  a  reviewed  author  may  be  wrong 
about  his  critic.  At  editor  frequently  makes  slight  insertions  or 
omissions — I  mean  slight  in  quantity  of  type — as  he  goes  over  the  last 
proof;  this  he  does  in  a  comparative  hurry,  and  it  may  chance  that  he 
does  not  know  the  full  sting  of  his  little  alteration.  The  very  bit  which 
the  writer  of  the  book  most  complains  of  may  not  have  been  seen  by  the 
person  who  is  called  the  writer  of  the  article  until  after  the  appearance 
of  the  journal ;  nay,  if  he  be  one  of  those — few,  I  daresay — who  do  not 
read  their  own  articles,  may  never  have  been  seen  by  him  at  all.  Pos- 
sibly, the  insertion  or  omission  would  not  have  been  made  if  the  editor 
could  have  had  one  minute's  conversation  with  his  contributor.  Some- 
times it  actually  contradicts  something  which  is  allowed  to  remain  in 
another  part  of  the  article ;  and  sometimes,  especially  in  the  case  of 
omission,  it  renders  other  parts  of  the  article  unintelligible.  These  are 
disadvantages  of  the  system,'  and  a  judicious  editor  is  not  very  free 
with  his  nuns  et  alter  pannus.  Next,  readers  in  general,  when  they 
see  the  pages  of  a  journal  with  the  articles  so  nicely  fitting,  and  so 
many  ending  with  the  page  or  column,  have  very  little  notion  of  the 
cutting  and  carving  which  goes  to  the  process.  At  the  very  last 
moment  arises  the  necessity  of  some  trimming  of  this  kind  ;  and  the 
editor,  who  would  gladly  call  the  writer  to  counsel  if  he  could,  is 
obliged  to  strike  out  ten  or  twenty  lines.  He  must  do  his  best,  but  it 
ma  v  chance  that  the  omission  selected  would  take  from  the  writer  the 


14  A  BUDGET   OF  PARADOXES. 

power  of  owning  the  article.  A  few  years  ago,  an  able  opponent  of 
mine  wrote  to  a  journal  some  criticisms  upon  an  article  which  he 
expressly  attributed  to  me.  I  replied  as  if  I  were  the  writer,  which,  in 
a  sense,  I  was.  But  if  any  one  had  required  of  me  an  unmodified  'Yes  ' 
or  '  No '  to  the  question  whether  I  wrote  the  article,  I  must,  of  two 
falsehoods,  have  chosen  '  No  :  '  for  certain  omissions,  dictated  by  the 
necessities  of  space  and  time,  would  have  amounted,  had  my  signature 
been  affixed,  to  a  silent  surrender  of  points  which,  in  my  own  cha- 
racter, I  must  have  strongly  insisted  on,  unless  I  had  chosen  to  admit 
certain  inferences  against  what  I  had  previously  published  in  my  own 
name.  I  may  here  add  that  the  forms  of  journalism  obliged  me  in  this 
case  to  remind  my  opponent  that  it  could  not  be  permitted  to  me,  in 
that  journal,  either  to  acknowledge  or  deny  the  authorship  of  the  articles. 
The  cautions  derived  from  the  above  remarks  are  particularly  wanted 
with  reference  to  the  editorial  comments  upon  letters  of  complaint. 
There  is  often  no  time  to  send  these  letters  to  the  contributor, 
and  even  when  this  can  be  done,  an  editor  is — and  very  properly — 
never  of  so  editorial  a  mind  as  when  he  is  revising  the  comments  of 
a  contributor  upon  an  assailant  of  the  article.  He  is  then  in  a  better 
position  as  to  information,  and  a  more  critical  position  as  to  responsi- 
bility. Of  course,  an  editor  never  meddles,  except  under  notice,  with 
the  letter  of  a  Correspondent,  whether  of  a  complainant,  of  a  casual  in- 
formant, or  of  a  contributor  who  sees  reason  to  become  a  correspondent. 
Omissions  must  sometimes  be  made  when  a  grievance  is  too  highly 
spiced.  It  did  once  happen  to  me  that  a  waggish  editor  made  an  inser- 
tion without  notice  in  a  letter  signed  by  me  with  some  fiction,  which 
insertion  contained  the  name  of  a  friend  of  mine,  with  a  satire  which  I 
did  not  believe,  and  should  not  have  written  if  I  had.  To  my  strong 
rebuke,  he  replied — '  I  know  it  was  very  wrong  ;  but  human  nature 
could  not  resist.'  But  this  was  the  only  occasion  on  which  such  a 
thing  ever  happened  to  me. 

I  daresay  what  I  have  written  may  give  some  of  your  readers  to  under- 
stand some  of  the  pericula  et  commoda  of  modern  journalism.  I  have 
known  men  of  deep  learning  and  science  as  ignorant  of  the  prevailing 
system  as  any  uneducated  reader  of  a  newspaper  in  a  country  town.  I 
may,  perhaps,  induce  some  writers  not  to  be  too  sure  about  this,  that, 
or  the  other  person.  They  may  detect  their  reviewer,  and  they  may  be 
safe  in  attributing  to  him  the  general  matter  and  tone  of  the  article. 
But  about  one  and  another  point,  especially  if  it  be  a  short  and  sting- 
ing point,  they  may  very  easily  chance  to  be  wrong.  It  has  happened 
to  myself,  and  within  a  few  weeks  to  publication,  to  be  wrong  in  two 
ways  in  reading  a  past  article — to  attribute  to  editorial  insertion  what 
was  really  my  own,  and  to  attribute  to  myself  what  was  really  editorial 
insertion. 

What  is  a  man  to  do  who  is  asked  whether  he  wrote  an  article. 
He  may,  of  course,  refuse  to  answer ;  which,  is  regarded  as  an 


INTRODUCTORY.  15 

admission.  He  may  say,  as  Swift  did  to  Serjeant  Bettesworth, 
'  Sir,  when  I  was  a  young  man,  a  friend  of  mine  advised  me, 
whenever  I  was  asked  whether  I  had  written  a  certain  paper,  to 
deny  it ;  and  I  accordingly  tell  you  that  I  did  not  write  it.'  He 
may  say,  as  I  often  do,  when  charged  wit.li  having  invented  a  joke, 
story,  or  epigram,  '  I  wa*nt  all  the  credit  I  can  get,  and  therefore 
I  always  acknowledge  all  that  is  attributed  to  me,  truly  or  not ; 
the  story,  £c.  is  mine.  But  for  serious  earnest,  in  the  matter  of 
imputed  criticism,  the  answer  may  be,  '  That  article  was  of  my 
material,  but  the  editor  has  not  let  it  stand  as  I  gave  it ;  I  cannot 
own  it  as  a  whole.'  He  may  then  refuse  to  be  particular  as  to 
the  amount  of  the  editor's  interference.  Of  this  there  are  two 
extreme  cases.  The  editor  may  have  expunged  nothing  but  a 
qualifying  adverb.  Or  he  may  have  done  as  follows.  We  all 
remember  the  account  of  Adam  which  satirizes  woman,  but 
eulogizes  her  if  every  second  and  third  line  be  transposed.  As 
in — 

Adam  could  find  no  solid  peace 

When  Eve  was  given  him  for  a  mate, 

Till  lie  beheld  a  woman's  face, 
Adam  was  in  a  happy  state. 

If  this  had  been  the  article,  and  a  gallant  editor  had  made  the 
transpositions,  the  author  could  not  with  truth  acknowledge.  If 
the  alteration  were  only  an  omitted  adverb,  or  a  few  things  of  the 
sort,  the  author  could  not  with  truth  deny.  In  all  that  comes 
between,  eveiy  man  must  be  his  own  casuist.  I  stared,  when  I 
was  a  boy,  to  hear  grave  persons  approve  of  Sir  Walter  Scott's 
downright  denial  that  he  was  the  author  of  Waverley,  in  answer 
to  the  Prince  Regent's  downright  question.  If  I  remember 
rightly,  Samuel  Johnson  would  have  approved  of  the  same  course. 
It  is  known  that,  whatever  the  law  gives,  it  also  gives  all  that 
is  necessary  to  full  possession  ;  thus  a  man  whose  land  is  environed 
by  the  land  of  others  has  a  right  of  way  over  the  land  of  these 
others.  By  analogy,  it  is  argued  that  when  a  man  has  a  right  to 
his  secret,  he  has  a  right  to  all  that  is  necessary  to  keep  it,  and 
that  is  not  unlawful.  If,  then,  he  can  only  keep  his  secret  by 
denial,  he  has  a  right  to  denial.  This  I  admit  to  be  an  answer  as 
against  all  men  except  the  denier  himself;  if  conscience  and  self- 
respect  will  allow  it,  no  one  can  impeach  it.  But  the  question 
cannot  be  solved  on  a  case.  That  question  is,  A  lie,  is  it  malum  in 
se,  without  reference  to  meaning  and  circumstances  ?  This  is  a 
question  with  two  sides  to  it.  Cases  may  be  invented  in  which  a 


16  A   BUDGET   OF   PARADOXES. 

lie  is  the  only  way  of  preventing  a  murder,  or  in  which  a  lie  may 
otherwise  save  a  life.  In  these  cases  it  is  difficult  to  acquit,  and 
almost  impossible  to  blame  ;  discretion  introduced,  the  line  be- 
comes very  hard  to  draw. 

I  know  but  one  work  which  has  precisely — as  at  first  appears — 
the  character  and  object  of  my  Budget.  It  is  the  '  Eeview  of  the 
Works  of  the  Eoyal  Society  of  London,'  by  Sir  John  Hill,  M.D. 
(1751  and  1780,  4to.)  This  man  offended  many:  the  Eoyal 
Society,  by  his  work ;  the  medical  profession,  by  inventing  and 
selling  extra-pharmacopceian  doses  ;  Grarrick,  by  resenting  the 
rejection  of  a  play.  So  Grarrick  wrote: 

For  physic  and  farces  his  equal  there  scarce  is  ; 
His  farces  are  physic ;  his  physic  a  farce  is. 

I  have  fired  at  the  Eoyal  Society  and  at  the  medical  profession, 
but  I  have  given  a  wide  berth  to  the  drama  and  its  wits  ;  so 
there  is  no  epigram  out  against  me,  as  yet.  He  was  very  able 
and  very  eccentric.  Dr.  Thomson  (Hist.  Roy.  Soc.~)  says  he  has 
no  humour,  but  Dr.  Thomson  was  a  man  who  never  would  have 
discovered  humour. 

Mr.  Weld  (Hist.  Roy.  Soc.}  backs  Dr.  Thomson,  but  with  a  re- 
markable addition.  Having  followed  his  predecessor  in  observing 
that  the  Transactions  in  Martin  Folkes's  time  have  an  unusual 
proportion  of  trifling  and  puerile  papers,  he  says  that  Hill's  book 
is  a  poor  attempt  at  humour,  and  glaringly  exhibits  the  feelings 
of  a  disappointed  man.  It  is  probable,  he  adds,  that  the  points 
told  with  some  effect  on  the  Society  ;  for  shortly  after  its  publica- 
tion the  Transactions  possess  a  much  higher  scientific  value. 

I  copy  an  account  which  I  gave  elsewhere. 

When  the  Eoyal  Society  was  founded,  the  Fellows  set  to  work 
to  prove  all  things,  that  they  might  hold  fast  that  which  was 
good.  They  bent  themselves  to  the  question  whether  sprats  were 
young  herrings.  They  made  a  circle  of  the  powder  of  a  unicorn's 
horn,  and  set  a  spider  in  the  middle  of  it ;  '  but  it  immediately 
ran  out.'  They  tried  several  times,  and  the  spider  '  once  made 
some  stay  in  the  powder.'  They  enquired  into  Kenelm  Digby's 
sympathetic  powder.  '  Magnetical  cures  being  discoursed  of,  Sir 
Gilbert  Talbot  promised  to  communicate  what  he  knew  of  sym- 
pathetical  cures  ;  and  those  members  who  had  any  of  the  powder 
of  sympathy,  were  desired  to  bring  some  of  it  at  the  next  meeting.' 

June  21,  1661,  certain  gentlemen  were  appointed  '  curators  of 
the  proposal  of  tormenting  a  man  with  the  sympathetic  powder ; ' 
I  cannot  find  any  record  of  the  result.  And  so  they  went  on 


INTRODUCTORY.  1 7 

until  the  time  of  Sir  John  Hill's  satire,  in  1751.  This  once  well- 
known  work  is,  in  my.  judgment,  the  greatest  compliment  the 
Royal  Society  ever  received.  It  brought  forward  a  number  of 
what  are  now  feeble  and  childish  researches  in  the  Philosophical 
Transactions.  It  showed  that  the  inquirers  had  actually  been 
inquiring;  and  that  they  did  not  pronounce  decision  about 
'natural  knowledge'  by  help  of  '  natural  knowledge.'  But  for 
this,  Hill  would  neither  have  known  what  to  assail,  nor  how. 
Matters  are  now  entirely  changed.  The  scientific  bodies  are  far 
too  well  established  to  risk  themselves.  Iblt  qui  zonam  perdidit — 

Let  him  take  castles  who  lias  ne'er  a  gi-oafc. 

These  great  institutions  are  now  without  any  collective  purpose, 
except  that  of  promoting  individual  energy  ;  they  print  for  their 
contributors,  and  guard  themselves  by  a  general  declaration  that 
they  will  not  be  answerable  for  the  things  they  print.  Of  course 
they  will  not  put  forward  anything  for  everybody ;  but  a  writer  of 
a  certain  reputation,  or  matter  of  a  certain  look  of  plausibility  and 
safety,  will  find  admission.  This  is  as  it  should  be  ;  the  pas- 
turer  of  flocks  and  herds  and  the  hunters  of  wild  beasts  are  two 
very  different  bodies,  with  very  different  policies.  The  scientific 
academies  are  what  a  spiritualist  might  call  'publishing  mediums,' 
and  their  spirits  fall  occasionally  into  writing  which  looks  as  if 
minds  in  the  higher  state  were  not  always  impervious  to  nonsense. 

The  following  joke  is  attributed  to  Sir  John  Hill.  I  cannot 
honestly  say  I  believe  it ;  but  it  shows  that  his  contemporaries  did 
not  believe  he  had  no  humour.  Good  stories  are  always  in  some 
sort  of  keeping  with  the  characters  on  which  they  are  fastened. 
•Sir  John  Hill  contrived  a  communication  to  the  Royal  Society 
from  Portsmouth,  to  the  effect  that  a  sailor  had  broken  his  leg  in 
a  fall  from  the  mast-head  ;  that  bandages  and  a  plentiful  applica- 
tion of  tarwater  had  made  him,  in  three  days,  able  to  use  his  leg 
as  well  as  ever.  While  this  communication  was  under  grave 
discussion — it  must  be  remembered  that  many  then  thought  tar- 
water  had  extraordinary  remedial  properties — the  joker  contrived 
that  a  second  letter  should  be  delivered,  which  stated  that  the 
writer  had  forgotten,  in  his  previous  communication,  to  mention 
that  the  leg  was  a  wooden  leg !  Horace  Walpole  told  this  story, 
I  suppose  for  the  first  time  ;  he  is  good  authority  for  the  fact  of 
circulation,  but  for  nothing  more. 

Sir  John  Hill's  book  is  droll  and  cutting  satire.  Dr.  Maty, 
(Sec.  Royal  Society)  wrote  thus  of  it  in  the  Journal  Britannique 
(Feb.  1751),  of  which  he  was  editor: 

c 


18  A  BUDGET   OF  PAEADOXES. 

H  est  facheux  que  cet  ingenieux  Naturaliste,  qui  nous  a  deja  donne 
et  qui  nous  prepare  encore  des  ouvrages  plus  utiles,  empioie  a  cette 
odieuse  tache  une  plume  qu'il  trempe  dans  le  fiel  et  dans  1' absinthe.  II 
est  vrai  que  plusieurs  de  ses  remarques  sont  fondees,  et  qu'a  1'erreur 
qu'il  indique,  il  joint  en  meme  terns  la  correction.  Mais  il  n'est  pas  tou- 
jours  equitable,  et  ne  manque  jamais  d'insulter.  Que  peut  apres  tout 
prouver  son  livre,  si  ce  n'est  que  la  quarante-cinquieme  partie  d'un 
tres-ample  et  tres-utile  Becueil  n'est  pas  exempte  d'erreurs  ?  Devoit- 
il  confondre  avec  des  Ecrivains  superficiels,  dont  la  Liberte  du  Corps  ne 
permet  pas  de  restreindre  la  fertilite,  cette  foule  de  savans  du  Premier 
ordre,  dont  les  Merits  ont  orne  et  ornent  encore  les  Transactions  ?  A-t-il 
oublie  qu'on  j  a  vu  frequemment  les  noms  des  Boyle,  des  Newton, 
des  Halley,  des  De  Moivres,  des  Hans  Sloane,  etc.  ?  Et  qu'on  y  trouve 
encore  ceux  des  Ward,  des  Bradley,  des  Graham,  des  Ellicot,  des  Watson, 
et  d'un  Auteur  que  Mr.  Hill  prefere  a  tous  les  autres,  je  veux  dire  de 
Mr.  Hill  lui-meme  ? 

This  was  the  only  answer  ;  but  it  was  no  answer  at  all.  Hill's 
object  was  to  expose  the  absurdities ;  he  therefore  collected  the 
absurdities.  I  feel  sure  that  Hill  was  a  benefactor  of  the  Royal 
Society ;  and  much  more  than  he  would  have  been  if  he  had 
softened  their  errors  and  enhanced  their  praises.  No  reviewer 
will  object  to  me  that  I  have  omitted  Young,  Laplace,  &c.  But 
then  my  book  has  a  true  title.  Hill  should  not  have  called  his 
a  review  of  the  '  Works.' 

It  was  charged  against  Sir  John  Hill  that  he  had  tried  to 
become  a  Fellow  of  the  Royal  Society  and  had  failed.  This  he 
denied,  and  challenged  the  production  of  the  certificate  which  a 
candidate  always  sends  in,  and  which  is  preserved.  But  perhaps 
he  could  not  get  so  far  as  a  certificate — that  is,  could  not  find  any 
one  to  recommend  him ;  he  was  a  likely  man  to  be  in  such  a 
predicament.  As  I  have  myself  run  foul  of  the  Society  on  some 
little  points,  I  conceive  it  possible  that  I  may  fall  under  a  like 
suspicion.  Whether  I  could  have  been  a  Fellow,  I  cannot  know  ; 
as  the  gentleman  said  who  was  asked  if  he  could  play  the  violin, 
I  never  tried.  I  have  always  had  a  high  opinion  of  the  Society 
upon  its  whole  history.  A  person  used  to  historical  inquiry 
learns  to  look  at  wholes  ;  the  Universities  of  Oxford  and 
Cambridge,  the  College  of  Physicians,  &c.  are  taken  in  all  their 
duration.  But  those  who  are  not  historians — I  mean  not 
possessed  of  the  habit  of  history — hold  a  mass  of  opinions  about 
current  things  which  lead  them  into  all  kinds  of  confusion  when 
they  try  to  look  back.  SN"ot  to  give  an  instance  which  will  offend 
any  set  of  existing  men — this  merely  because  I  can  do  without 
it — let  us  take  the  country  at  large.  Magna  Charta  for  ever  ! 


INTRODUCTORY.  19 

glorious  safeguard  of  our  liberties  !  Nullus  liber  homo  capiatur 
aut  imprisonetur,.  .  .  .  aut  aliquo  modo  destruatur,  nisi  per 
judicium  parium.  .  .  .  Liber  homo;  frank  home;  a  capital 
thing  for  him — but  how  about  the  villeins  ?  Oh,  there  are  none 
noiv !  But  there  were.  Who  cares  for  villains,  or  barbarians,  or 
helots  ?  And  so  England,  and  Athens,  and  Sparta,  were  free 
States  :  all  the  freemen  in  them  were  free.  Long  after  Magna 
Charta,  villains  were  sold  with  their  *  chattels  and  offspring,' 
named  in  that  order.  Long  after  Magna  Charta,  it  was  law  that 
'  Le  Seigniour  poit  rob,  naufrer,  et  chastiser  son  villein  a  son 
volunt,  salve  que  il  ne  poit  luy  maim.' 

The  Eoyal  Society  was  founded  as  a  co-operative  body,  and  co- 
operation was  its  purpose.  The  early  charters,  &c.  do  not  contain 
a  trace  of  the  intention  to  create  a  scientific  distinction,  a  kind 
of  Legion  of  Honour.  It  is  clear  that  the  qualification  was  ability 
and  willingness  to  do  good  work  for  the  promotion  of  natural 
knowledge,  no  matter  in  how  many  persons,  nor  of  what  position 
in  society.  Charles  II.  gave  a  smart  rebuke  for  exclusiveness,  as 
elsewhere  mentioned.  In  time  arose,  almost  of  course,  the  idea 
of  distinction  attaching  to  the  title  ;  and  when  I  first  began 
to  know  the  Society,  it  was  in  this  state.  Gentlemen  of  good 
social  position  were  freely  elected  if  they  were  really  educated 
men  ;  but  the  moment  a  claimant  was  announced  as  resting  on 
his  science,  there  was  a  disposition  to  inquire  whether  he  was 
scientific  enough.  The  maxim  of  the  poet  was  adopted  ;  and 
the  Fellows  were  practically  jdivided  into  Drink-deeps  and 
Taste-nots. 

I  was,  in  early  life,  much  repelled  by  the  tone  taken  by  the 
Fellows  of  the  Society  with  respect  to  their  very  mixed  body.  A 
man  high  in  science — some  thirty-seven  years  ago  (about  1830) — 
gave  me  some  encouragement,  as  he  thought.  '  We  shall  have  you  a 
Fellow  of  the  Royal  Society  in  time,'  said  he.  Umph  !  thought  I : 
for  I  had  thatday  heard  of  some  recent  elections,  the  united  science 
of  which  would  not  have  demonstrated  I.  1,  nor  explained  the  action 
of  a  pump.  Truly  an  elevation  to  look  up  at !  It  came,  further,  to 
my  knowledge  that  the  Royal  Society — if  I  might  judge  by  the 
claims  made  by  very  influential  Fellows — considered  itself  as 
entitled  to  the  best  of  everything :  second-best  being  left  for  the 
newer  bodies.  A  secretary,  in  returning  thanks  for  the  Royal 
at  an  anniversary  of  the  Astronomical,  gave  rather  a  lecture  to 
the  company  on  the  positive  duty  of  all  present  to  send  the  very 
best  to  the  old  body,  and  the  absolute  right  of  the  old  body  to 
expect  it.  An  old  friend  of  mine,  on  a  similar  occasion,  stated  as 

c  2 


20  A  BUDGET   OF  PAEADOXES. 

a  fact  that  the  thing  was  always  done,  as  well  as  that  it  ought  to 
be  done. 

Of  late  years  this  pretension  has  been  made  by  a  President 
of  the  Society.  In  1855,  Lord  Eosse  presented  a  confidential 
memorandum  to  the  Council  on  the  expediency  of  enlarging 
their  number.  He  says,  '  In  a  Council  so  small  it  is  impossible 
to  secure  a  satisfactory  representation  of  the  leading  scientific 
Societies,  and  it  is  scarcely  to  be  expected  that,  under  such  cir- 
cumstances, they  will  continue  to  publish  inferior  papers  while 
they  send  the  best  to  our  Transactio'iis.'1 

And,  again,  with  all  the  Societies  represented  on  the  Council, 
1  even  if  every  Science  had  its  Society,  and  if  they  published  every- 
thing, withholding  their  best  papers  [i.e.  from  the  Eoyal  Society], 
which  they  would  not  be  likely  to  do,  still  there  would  remain  to 
the  Eoyal  Society  .  .  .'  Lord  Eosse  seems  to  imagine  that  the 
minor  Societies  themselves  transfer  their  best  papers  to  the 
Eoyal  Society  ;  that  if,  for  instance,  the  Astronomical  Society 
were  to  receive  from  A.  B.  a  paper  of  unusual  merit,  the  Society 
would  transfer  it  to  the  Eoyal  Society.  This  is  quite  wrong :  any 
preference  of  the  Eoyal  to  another  Society  is  the  work  of  the 
contributor  himself.  But  it  shows  how  well  hafted  is  the  Eoyal 
Society's  claim,  that  a  President  should  acquire  the  notion  that 
it  is  acknowledged  and  acted  upon  by  the  other  Societies,  in  their 
joint  and  corporate  capacities.  To  the  pretension  thus  made  I 
never  could  give  any  sympathy.  When  I  first  heard  Mr.  Christie, 
Sec.  E.  S.,  set  it  forth  at  the  anniversary  dinner  of  the  Astro- 
nomical Society,  I  remembered  the  Baron  in  Walter  Scott — 

Of  Gilbert  the  Galliard  a  heriot  lie  sought, 
Saying,  Give  thy  best  steed  as  a  vassal  ought. 

And  I  remembered  the  answer — 

Lord  and  Earl  though  thou  be,  I  trow 
I  can  rein  Buck's-foot  better  than  thou. 

Fully  conceding  that  the  Eoyal  Society  is  entitled  to  pre- 
eminent rank  and  all  the  respect  due  to  age  and  services,  I 
could  not,  nor  can  I  now,  see  any  more  obligation  in  a  contributor 
to  send  his  best  to  that  Society  than  he  can  make  out  to  be  due 
to  himself.  This  pretension,  in  my  mind,  was  hooked  on,  by 
my  historical  mode  of  viewing  things  already  mentioned,  to  my 
knowledge  of  the  fact  that  the  Eoyal  Society — the  chief  fault, 
perhaps,  lying  with  its  President,  Sir  Joseph  Banks — had  sternly 
set  itself  against  the  formation  of  other  societies  ;  the  Geological 


INTRODUCTORY.  21 

and  Astronomical,  for  instance,  though  it  must  be  added  that 
the  chief  rebels  came  out  of  the  Society  itself.  And  so  a  certain 
not  very  defined  dislike  was  generated  in  my  mind — an  anti- 
aristocratic  affair — to  the  body  which  seemed  to  me  a  little  too 
uplifted.  This  would,  I  daresay,  have  worn  off;  but  a  more 
formidable  objection  arose.  My  views  of  physical  science  gradu- 
ally arranged  themselves  into  a  form  which  would  have  rendered 
F.R.S.,  as  attached  to  my  name,  a  false  representation  symbol. 
The  Royal  Society  is  the  great  fortress  of  general  physics :  and  in 
the  philosophy  of  our  day,  as  to  general  physics,  there  is  some- 
thing which  makes  the  banner  of  the  R.S.  one  under  which  I 
cannot  march.  Everybody  who  saw  the  three  letters  after  my 
name  would  infer  certain  things  as  to  my  mode  of  thought  which 
would  not  be  true  inference.  It  would  take  much  space  to  explain 
this  in  full.  I  may  hereafter,  perhaps,  write  a  budget  of  collected 
results  of  the  a  priori  philosophy,  the  nibbling  at  the  small 
end  of  omniscience,  and  the  effect  it  has  had  on  common  life, 
from  the  family  parlour  to  the  jury-box,  from  the  girls'-school 
to  the  vestry -meeting.  There  are  in  the  Society  those  who 
would,  were  there  no  others,  prevent  my  criticism,  be  its  con- 
clusions true  or  false,  from  having  any  basis ;  but  they  are  in  the 
minority. 

There  is  no  objection  to  be  made  to  the  principles  of  philosophy 
in  vogue  at  the  Society,  when  they  are  stated  as  principles  ;  but 
there  is  an  omniscience  in  daily  practice  which  the  principles 
repudiate.  In  like  manner,  the  most  retaliatory  Christians  have 
a  perfect  form  of  round  words  about  behaviour  to  those  who 
injure  them :  none  of  them  are  as  candid  as  a  little  boy  I  knew, 
who,  to  his  mother's  admonition,  You  should  love  your  enemies, 
answered — Catch  me  at  it ! 

Years  ago,  a  change  took  place  which  would  alone  have  put  a 
sufficient  difficulty  in  the  way.  The  co-operative  body  got  tired 
of  getting  funds  from  and  lending  name  to  persons  who  had  little 
or  no  science,  and  wanted  F.R.S.  to  be  in  every  case  a  Fellow 
Really  Scientific.  Accordingly,  the  number  of  yearly  elections  was 
limited  to  fifteen  recommended  by  the  Council,  unless  the  general 
body  should  choose  to  elect  more  ;  which  it  does  not  do.  The 
election  is  now  a  competitive  examination :  it  is  no  longer — Are  you 
able  and  willing  to  promote  natural  knowledge  ;  it  is — Are  you  one 
of  the  upper  fifteen  of  those  who  make  such  claim.  In  the  list  of 
candidates — a  list  rapidly  growing  in  number — each  year  shows 
from  thirty  to  forty  of  those  whom  Newton  and  Boyle  would  have 
gladly  welcomed  as  fellow-labourers.  And  though  the  rejected 


22  A  BUDGET   OF  PAKADOXES. 

of  one  year  may  be  the  accepted  of  the  next — or  of  the  next  but 
one,  or  but  two,  if  self-respect  will  permit  the  candidate  to  hang 
on — yet  the  time  is  clearly  coming  when  many  of  those  who 
ought  to  be  welcomed  will  be  excluded  for  life,  or  else  shelved  at 
last,  when  past  work,  with  a  scientific  peerage.  Coupled  with 
this  attempt  to  create  a  kind  of  order  of  knighthood  is  'an  ab- 
surdity so  glaring  that  it  should  always  be  kept  before  the  general 
eye.  This  distinction,  this  mark  set  by  science  upon  successful 
investigation,  is  of  necessity  a  class-distinction.  Rowan  Hamilton, 
one  of  the  greatest  names  of  our  day  in  mathematical  science, 
never  could  attach  F.R.S.  to  his  name — he  could  not  afford  it. 
There  is  a  condition  precedent — Four  Red  Sovereigns.  It  is 
four  pounds  a  year,  or — to  those  who  have  contributed  to  the 
Transactions — forty  pounds  down.  This  is  as  it  should  be :  the 
Society  must  be  supported.  But  it  is  not  as  it  should  be  that  a 
kind  of  title  of  honour  should  be  forged,  that  a  body  should  take 
upon  itself  to  confer  distinctions  for  science,  when  it  is  in  the 
background — and  kept  there  when  the  distinction  is  trumpeted — 
that  the  wearer  is  a  man  who  can  spare  four  pounds  a  year.  I 
am  well  aware  that  in  England  a  person  who  is  not  gifted,  either 
by  nature  or  art,  with  this  amount  of  money  power,  is,  with  the 
mass,  a  very  second-rate  sort  of  Newton,  whatever  he  may  be  in 
the  field  of  investigation.  Even  men  of  science,  so  called,  have 
this  feeling.  I  know  that  the  scientific  advisers  of  the  Admiralty, 
who,  years  ago,  received  100£.  a  year  each  for  his  trouble,  were 
sneered  at  by  a  wealthy  pretender  as  '  fellows  to  whom  a  hundred 
a  year  is  an  object.'  Dr.  Thomas  Young  was  one  of  them.  To 
a  bookish  man — I  mean  a  man  who  can  manage  to  collect  books — 
there  is  no  tax.  To  myself,  for  example,  40L  worth  of  books 
deducted  from  my  shelves,  and  the  life-use  of  the  Society's 
splendid  library  instead,  would  have  been  a  capital  exchange. 
But  there  may  be,  and  are,  men  who  want  books,  and  cannot  pay 
the  Society's  price.  The  Council  would  be  very  liberal  in  allow- 
ing their  books  to  be  consulted.  I  have  no  doubt  that  if  a  known 
investigator  were  to  call  and  ask  to  look  at  certain  books,  the 
Assistant-Secretary  would  forthwith  seat  him  with  the  books 
before  him,  absence  of  F.R.S.  not  in  any  wise  withstanding.  But 
this  is  not  like  having  the  right  to  consult  any  book  on  any  day, 
and  to  take  it  away,  if  farther  wanted. 

So  much  for  the  Royal  Society  as  concerns  myself.  I  must  add, 
that  there  is  not  a  spark  of  party  feeling  against  those  who 
wilfully  remain  outside.  The  better  minds  of  course  know  better; 
and  the  smaller  savants  look  complacently  on  the  idea  of  an 


INTRODUCTORY.  23 

outer  world  which  makes  elite  of  them.  I  have  done  such  a 
thing  as  serve  on  a  committee  of  the  Society,  and  report  on  a 
paper :  they  had  the  sense  to  ask,  and  I  had  the  sense  to  see  that 
none  of  my  opinions  were  compromised  by  compliance.  And  I 
will  be  of  any  use  which  does  not  involve  the  status  of  homo  trium 
tiierarum ;  as  I  have  elsewhere  explained,  I  would  gladly  be 
Fautor  Realis  Scientice,  but  I  would  not  be  taken  for  Falsce 
Ra'ioiiis  Sacerdos. 

Nothing  worse  will  ever  happen  to  me  than  the  smile  which 
individuals  bestow  on  a  man  who  does  not  groove.  Wisdom,  like 
religion,  belongs  to  majorities  ;  who  can  wonder  that  it  should  be 
so  thought,  when  it  is  so  clearly  pictured  in  the  New  Testament 
from  one  end  to  the  other  ? 

The  counterpart  of  paradox,  the  isolated  opinion  of  one  or  of 
few,  is  the  general  opinion  held  by  all  the  rest ;  and  the  counter- 
part of  false  and  absurd  paradox  is  what  is  called  the  '  vulgar 
error,'  the  pseudodox.  There  is  one  great  work  on  this  last  subject, 
the  Pseudodoxia  Epidemica  of  Sir  Thomas  Browne,  the  famous 
author  of  the  Religio  Medici:,  it  usually  goes  by  the  name  of 
Browne '  On  Vulgar  Errors '  (1st  ed.  1646  ;  6th,  1672).  A  careful 
analysis  of  this  work  would  show  that  vulgar  errors  are  frequently 
opposed  by  scientific  errors  ;  but  good  sense  is  always  good  sense, 
and  Browne's  book  has  a  vast  quantity  of  it. 

As  an  example  of  bad  philosophy  brought  against  bad  observa- 
tion. The  Amphisbsena  serpent  was  supposed  to  have  two  heads, 
one  at  each  end ;  partly  from  its  shape,  partly  because  it  runs 
backwards  as  well  as  forwards.  On  this  Sir  Thomas  Browne  makes 
the  following  remarks : — 

And  were  there  any  such  species  or  natural  kind  of  animal,  it  would 
be  hard  to  make  good  those  six  positions  of  body  which,  according  to 
the  three  dimensions,  are  ascribed  unto  every  Animal ;  that  is,  infra, 
supra,  ante,  retro,  dextrosum,  sinistrosum :  for  if  (as  it  is  determined) 
that  be  the  anterior  and  upper  part  wherein  the  senses  are  placed,  and 
that  the  posterior  and  lower  part  which  is  opposite  thereunto,  there  is 
no  inferior  or  former  part  in  this  Animal ;  for  the  senses,  being  placed 
at  both  extreams,  doth  make  both  ends  anterior,  which  is  impossible ; 
the  terms  being  Relative,  which  mutually  subsist,  and  are  not  without 
each  other.  And  therefore  this  duplicity  was  ill  contrived  to  place  one 
head  at  both  extreams,  and  had  been  more  tolerable  to  Lave  settled 
three  or  four  at  one.  And  therefore  also  Poets  have  been  more  reason- 
able than  Philosophers,  and  Geryon  or  Cerberus  less  monstrous  than 
Amphitbcentk 

There  may  be  paradox  upon  paradox :  and  there  is  a  good 
instance  in  the  eighth  century  in  the  case  of  Virgil,  an  Irishman, 


24  A   BUDGET   OF  PARADOXES. 

Bishop  of  Salzburg  and  afterwards  Saint,  and  his  quarrels  with 
Boniface,  an  Englishman,  Archbishop  of  Mentz,  also  afterwards 
Saint.  All  we  know  about  the  matter  is,  that  there  exists  a 
letter  of  748  from  Pope  Zachary,  citing  Virgil — then,  it  seems,  at 
most  a  simple  priest,  though  the  Pope  was  not  sure  even  of  that 
— to  Eome  to  answer  the  charge  of  maintaining  that  there  is 
another  world  (mundus)  under  our  earth  (terra),  with  another 
sun  and  another  moon.  Nothing  more  is  known :  the  letter 
contains  threats  in  the  event  of  the  charge  being  true ;  and  there 
history  drops  the  matter.  Since  Virgil  was  afterwards  a  Bishop 
and  a  Saint,  we  may  fairly  conclude  that  he  died  in  the  full 
flower  of  orthodox  reputation.  It  has  been  supposed  —  and  it 
seems  probable — that  Virgil  maintained  that  the  earth  is  peopled 
all  the  way  round,  so  that  under  some  spots  there  are  antipodes ; 
that  his  contemporaries,  with  very  dim  ideas  about  the  roundness 
of  the  earth,  and  most  of  them  with  none  at  all,  interpreted  him 
as  putting  another  earth  under  ours — turned  the  other  way, 
probably,  like  the  second  piece  of  bread-and-butter  in  a  sandwich, 
with  a  sun  and  moon  of  its  own.  In  the  eighth  century  this 
would  infallibly  have  led  to  an  underground  Gospel,  an  under- 
ground Pope,  and  an  underground  Avignon  for  him  to  live  in. 
When,  in  later  times,  the  idea  of  inhabitants  for  the  planets 
was  started,  it  was  immediately  asked  whether  they  had  sinned, 
whether  Jesus  Christ  died  for  them,  whether  their  wine  and  their 
water  could  be  lawfully  used  in  the  sacraments,  &c. 

On  so  small  a  basis  as  the  above  has  been  constructed  a  com- 
panion case  to  the  persecution  of  Galileo.  On  one  side  the 
positive  assertion,  with  indignant  comment,  that  Virgil  was 
deposed  for  antipodal  heresy,  on  the  other,  serious  attempts  at 
justification,  palliation,  or  mystification.  Some  writers  say  that 
Virgil  was  found  guilty ;  others  that  he  gave  satisfactory  expla- 
nation, and  became  very  good  friends  with  Boniface :  for  all 
which  see  Bayle.  Some  have  maintained  that  the  antipodist  was 
a  different  person  from  the  canonised  bishop :  there  is  a  second 
Virgil,  made  to  order.  When  your  shoes  pinch,  and  will  not 
stretch,  always  throw  them  away  and  get  another  pair :  the  same 
with  your  facts.  Baronius  was  not  up  to  the  plan  of  a  substitute  : 
his  commentator  Pagi  (probably  writing  about  1690)  argues  for 
it  in  a  manner  which  I  think  Baronius  would  not  have  approved. 
This  Virgil  was  perhaps  a  slippery  fellow.  The  Pope  says  he 
hears  that  Virgil  pretended  licence  from  him  to  claim  one  of 
some  new  bishoprics  :  this  he  declares  is  totally  false.  It  is  part 
of  the  argument  that  such  a  man  as  this  could  not  have  been 


INTRODUCTOKY.  25 

created  a  Bishop  and  a  Saint:  on  this  point  there  will  be  opinions 
and  opinions.1 

Lactantius,  four  centuries  before,  had  laughed  at  the  antipodes 
in  a  manner  which  seems  to  be  ridicule  thrown  on  the  idea  of  the 
earth's  roundness.      Ptolemy,  without  reference  to  the  antipodes, 
describes  the  extent  of  the  inhabited  part  of  the  globe  in  a  way 
which  shows  that  he  could  have  had  no  objection  to  men  turned 
opposite  ways.     Probably,  in  the  eighth  century,  the  roundness  of 
the  earth  was  matter  of  thought  only  to  astronomers.      It  should 
always  be  remembered,  especially  by  those  who  affirm  persecution 
of  a  true  opinion,  that  but  for  our  knowing  from  Lactantius  that 
the   antipodal  notion  had   been  matter  of  assertion  and  denial 
among  theologians,  we  could  never  have  had  any  great  confidence 
in  Virgil  really  having  maintained  the  simple  theory  of  the  exist- 
ence of  antipodes.     And  even  now  we  are  not  entitled  to  affirm  it 
as  having  historical  proof:  the  evidence  goes  to  Virgil  having 
been  charged   with   very  absurd   notions,  which   it  seems  more 
likely  than   not  were  the   absurd  constructions   which  ignorant 
contemporaries  put  upon  sensible  opinions  of  his. 

One  curious  part  of  this  discussion  is,  that  neither  side  has 
allowed  Pope  Zachary  to  produce  evidence  to  character.      He 
shall  have  been  an  Urban,  say  the  astronomers ;  an  Urban  he 
ought  to  have  been,  say  the  theologians.     What  sort  of  man  was 
Zachary  ?     He  was  eminently  sensible  and  conciliatory  ;  he  con- 
trived to  make  northern  barbarians  hear  reason  in  a  way  which 
puts  him  high  among  that  section  of  the   early  popes  who  had 
the  knack  of  managing  uneducated  swordsmen.     He  kept  the 
peace  in  Italy  to  an  extent  which  historians  mention  with  ad- 
miration.     Even   Bale,  that  .Maharajah  of  pope-haters,   allows 
himself  to  quote  in  favour   of   Zachary,   that  'multa  Papalem 
dignitatem  decentia,  eademque  pra3clara  (scilicet)  opera  confecit.' 
And   this,   though    so  willing   to   find   fault  that,   speaking   of 
Zachary  putting  a  little  geographical  description   of  the   earth 
on  the  portico  of  the  Lateran  Church,  he  insinuates  that  it  was 
intended  to   affirm  that  the  Pope  was  lord  of  the  whole.     Nor 
can  he  say  how  long  Zachary  held  the  see,  except  by  announcing 
his  death  in  752,  '  cum  decem  annis  pestilentia?  sedi  praefuisset.' 

1  An  Irish  antiquary  informs  me  that  Virgil  is  mentioned  in  annals,  at  A.I/.  781,  as 
1  Verghil,  i.e.  the  geometer,  Abbot  of  Achadhbo  [and  Bishop  of  Saltzburg],  died  in 
Germany  in  the  thirteenth  year  of  his  bishoprick.'  No  allusion  is  made  to  his 
opinions ;  but  it  seems  he  was,  by  tradition,  a  mathematician.  The  Abbot  of  Aghabo 
(Queen's  County)  was  canonised  by  Gregory  IX.,  in  1233.  The  story  of  the  second, 
or  scapegoat,  Virgil  would  be  much  damaged  by  the  character  given  to  the  real 
bishop,  if  there  were  anything  in  it  to  dilapidate. 


26  A   BUDGET   OF   PARADOXES. 

There  was  another  quarrel  between  Virgil  and  Boniface  which 
is  an  illustration.  An  ignorant  priest  had  baptised  '  in^nomine 
Patriot,  et  Filia,  et  Spiritua  Sancta.'  Boniface  declared  the 
rite  null  and  void  ;  Virgil  maintained  the  contrary ;  and  Zachary 
decided  in  favour  of  Virgil,  on  the  ground  that  the  absurd  form 
was  only  ignorance  of  Latin,  and  not  heresy.  It  is  hard  to  believe 
that  this  man  deposed  a  priest  for  asserting  the  whole  globe  to 
be  inhabited.  To  me  the  little  information  that  we  have  seems 
to  indicate — but  not  with  certainty — that  Virgil  maintained  the 
antipodes :  that  his  ignorant  contemporaries  travestied  his  theory 
into  that  of  an  underground  cosmos  ;  that  the  Pope  cited  him 
to  Eome  to  explain  his  system,  which,  as  reported,  looked  like 
what  all  would  then  have  affirmed  to  be  heresy ;  that  he  gave 
satisfactory  explanations,  and  was  dismissed  with  honour.  It 
may  be  that  the  educated  Greek  monk,  Zachary,  knew  his 
Ptolemy  well  enough  to  guess  what  the  asserted  heretic  would 
say ;  we  have  seen  that  he  seems  to  have  patronised  geography. 
The  description  of  the  earth,  according  to  historians,  was  a  map  ; 
this  Pope  may  have  been  more  ready  than  another  to  prick  up  his 
ears  at  any  rumour  of  geographical  heresy,  from  hope  of  informa- 
tion. And  Virgil,  who  may  have  entered  the  sacred  presence  as 
frightened  as  Jacquard,  when  Napoleon  I.  sent  for  him  and  said, 
with  a  stern  voice  and  threatening  gesture,  '  You  are  the  man  who 
can  tie  a  knot  in  a  stretched  string,'  may  have  departed  as  well 
pleased  as  Jacquard  with  the  riband  and  pension  which  the  inter- 
view was  worth  to  him. 

A  word  more  about  Baronius.  If  he  had  been  pope,  as  he 
would  have  been  but  for  the  opposition  of  the  Spaniards,  and  if 
he  had  lived  ten  years  longer  than  he  did,  and  if  Clavius,  who 
would  have  been  his  astronomical  adviser,  had  lived  five  years 
longer  than  he  did,  it  is  probable,  nay  almost  certain,  that  the 
great  exhibition,  the  proceeding  against  Galileo,  would  not  have 
furnished  a  joke  against  theology  in  all  time  to  come.  For 
Baronius  was  sensible  and  witty  enough  to  say  that  in  the  Scrip- 
tures the  Holy  Spirit  intended  to  teach  how  to  go  to  Heaven, 
not  how  Heaven  goes ;  and  Clavius,  in  his  last  years,  confessed 
that  the  whole  system  of  the  heavens  had  broken  down,  and 
must  be  mended. 

The  manner  in  which  the  Galileo  case,  a  reality,  and  the 
Virgil  case,  a  fiction,  have  been  hawked  against  the  Eoman  see 
are  enough  to  show  that  the  Pope  and  his  adherents  have  not 
cared  much  about  physical  philosophy.  In  truth,  orthodoxy  has 


INTRODUCTORY.  27 

always  had  other  fish  to  fry.  Physics,  which  in  modern  times 
has  almost  usurped  the  name  philosophy,  in  England  at  least, 
has  felt  a  little  disposed  to  clothe  herself  with  all  the  honours 
of  persecution  which  belong  to  the  real  owner  of  the  name. 
But  the  bishops,  &c.  of  the  middle  ages  knew  that  the  contest 
between  nominalism  and  realism,  for  instance,  had  a  hundred 
times  more  bearing  upon  orthodoxy  than  anything  in  astronomy, 
&c.  A  wrong  notion  about  substance  might  play  the  mischief 
with  transubstantiation. 

The  question  of  the  earth's  motion  was  the  single  point  in 
which  orthodoxy  came  into  real  contact  with  science.  Many 
students  of  physics  were  suspected  of  magic,  many  of  atheism  :  but, 
stupid  as  the  mistake  may  have  been,  it  was  bond  fide  the  magic  or 
the  atheism,  not  the  physics,  which  was  assailed.  In  the  astro- 
nomical case  it  was  the  very  doctrine,  as  a  doctrine,  indepen- 
dently of  consequences,  which  was  the  corpus  delicti :  and  this 
because  it  contradicted  the  Bible.  And  so  it  did ;  for  the  stability 
of  the  earth  is  as  clearly  assumed  from  one  end  of  the  Old  Testa- 
ment to  the  other  as  the  solidity  of  iron.  Those  who  take  the 
Bible  to  be  totidem,  verbis  dictated  by  the  God  of  Truth  can 
refuse  to  believe  it;  and  they  make  strange  reasons.  They 
undertake,  a  prioi*i,  to  settle  Divine  intentions.  The  Holy  Spirit 
did  not  mean  to  teach  natural  philosophy :  this  they  know  before- 
hand ;  or  else  they  infer  it  from  finding  that  the  earth  does  move, 
and  the  Bible  says  it  does  not.  Of  course,  ignorance  apart,  every 
word  is  truth,  or  the  writer  did  not  mean  truth.  But  this  puts 
the  whole  book  on  its  trial :  for  we  never  can  find  out  what  the 
writer  meant,  until  we  otherwise  find  out  what  is  true.  Those 
who  like  may,  of  course,  declare  for  an  inspiration  over  which 
they  are  to  be  viceroys  ;  but  common  sense  will  either  accept 
verbal  meaning  or  deny  verbal  inspiration. 


28  A  BUDGET  OF  PARADOXES. 


Questiones  Morales,  folio,  1489  [Paris].     By  T.  Buridan. 

This  is  the  title  from  the  Hartwell  Catalogue  of  Law  Books.  I 
suppose  it  is  what  is  elsewhere  called  the  '  Commentary  on  the 
Ethics  of  Aristotle,'  printed  in  1489.  Buridan  (died  about  1358) 
is  the  creator  of  the  famous  ass  which,  as  Burdin's  ass,  was  cur- 
rent in  Burgundy,  perhaps  is,  as  a  vulgar  proverb.  Spinoza  says 
it  was  a  jenny  ass,  and  that  a  man  would  not  have  been  so  foolish  ; 
but  whether  the  compliment  is  paid  to  human  or  to  masculine 
character  does  not  appear — perhaps  to  both  in  one.  The  story 
told  about  the  famous  paradox  is  very  curious.  The  Queen  of 
France,  Joanna  or  Jeanne,  was  in  the  habit  of  sewing  her  lovers 
up  in  sacks,  and  throwing  them  into  the  Seine ;  not  for  blab- 
bing, but  that  they  might  not  blab — certainly  the  safer  plan. 
Buridan  was  exempted,  and,  in  gratitude,  invented  the  sophism. 
What  it  has  to  do  with  the  matter  has  never  been  explained. 
Assuredly  qui  facit  per  alium  facit  per  se  will  convict  Buridan 
of  prating.  The  argument  is  as  follows,  and  is  seldom  told  in 
full.  Buridan  was  for  free-will — that  is,  will  which  determines 
conduct,  let  motives  be  ever  so  evenly  balanced.  An  ass  is  equally 
pressed  by  hunger  and  by  thirst ;  a  bundle  of  hay  is  on  one  side, 
a  pail  of  water  on  the  other.  Surely,  you  will  say,  he  will  not  be 
ass  enough  to  die  for  want  of  food  or  drink  ;  he  will  then  make 
a  choice — that  is,  will  choose  between  alternatives  of  equal  force. 
The  problem  became  famous  in  the  schools  ;  some  allowed  the 
poor  donkey  to  die  of  indecision ;  some  denied  the  possibility  of 
the  balance,  which  was  no  answer  at  all. 

The  following  question  is  more  difficult,  and  involves  free-will 
to  all  who  answer — '  Which  you  please.'  If  the  northern  hemisphere 
were  land,  and  all  the  southern  hemisphere  water,  ought  we  to 
call  the  northern  hemisphere  an  island,  or  the  southern  hemisphere 
a  lake  ?  Both  the  questions  would  be  good  exercises  for  paradoxers 
who  must  be  kept  employed,  like  Michael  Scott's  devils.  The 
wizard  knew  nothing  about  squaring  the  circle,  &c.,  so  he  set 
them  to  make  ropes  out  of  sea  sand,  which  puzzled  them.  Stupid 
devils  !  much  of  our  glass  is  sea  sand,  and  it  makes  beautiful 
thread.  Had  Michael  set  them  to  square  the  circle  or  to  find 
a  perpetual  motion,  he  would  have  done  his  work  much  better. 
But  all  this  is  conjecture :  who  knows  that  I  have  not  hit  on  the 
very  plan  he  adopted  ?  Perhaps  the  whole  race  of  paradoxers 
on  hopeless  subjects  are  Michael's  subordinates,  condemned  to 
transmigration  after  transmigration,  until  their  task  is  done. 


THE   BUDGET   OPENED— BURIDAN.  29 

The  above  was  not  a  bad  guess.  A  little  after  the  time  when 
the  famous  Pascal  papers  were  produced,  I  came  into  possession 
of  a  correspondence  which,  but  for  these  papers,  I  should  have 
held  too  incredible  to  be  put  before  the  world.  But  when  one 
sheep  leaps  the  ditch,  another  will  follow  :  so  I  gave  the  following- 
account  in  the  Athenceum  of  October  5,  1867  : — 

The  recorded  story  is  that  Michael  Scott,  being  bound  by  contract 
to  procure  perpetual  employment  for  a  number  of  young  demons,  was 
worried  out  of  his  life  in  inventing  jobs  for  them,  until  at  last  he  set 
them  to  make  ropes  out  of  sea  sand,  which  they  never  could  do.  We 
have  obtained  a  very  curious  correspondence  between  the  wizard 
Michael  and  his  demon-slaves  ;  but  we  do  not  feel  at  liberty  to  say  how 
it  came  into  our  hands.  We  much  regret  that  we  did  not  receive  it 
in  time  for  the  British  Association.  It  appears  that  the  story,  true  as 
far  as  it  goes,  was  never  finished.  The  demons  easily  conquered  the 
rope  difficulty,  by  the  simple  process  of  making  the  sand  into  glass, 
and  spinning  the  glass  into  thread,  which  they  twisted.  Michael, 
thoroughly  disconcerted,  hit  upon  the  plan  of  setting  some  to  square 
the  circle,  others  to  find  the  perpetual  motion,  &c.  He  commanded 
each  of  them  to  transmigrate  from  one  human  body  into  another,  until 
their  tasks  were  done.  This  explains  the  whole  succession  of  cyclo- 
meters, and  all  the  heroes  of  the  Budget.  Some  of  this  correspondence 
is  very  recent ;  it  is  much  blotted,  and  we  are  not  quite  sure  of  its 
meaning  :  it  is  full  of  figurative  allusions  to  driving  something  illegible 
down  a  steep  into  the  sea.  It  looks  like  a  humble  petition  to  be 
allowed  some  diversion  iu  the  intervals  of  transmigration ;  and  the 

answer  is — 

Rumpat  et  serpens  iter  institutum, 

— a  line  of  Horace,  which  the  demons  interpret  as  a  direction  to  come 
athwart  the  proceedings  of  the  Institute  by  a  sly  trick.  Until  we  saw 
this,  we  were  suspicious  of  M.  Libri  :  the  unvarying  blunders  of  the 
correspondence  look  like  knowledge.  To  be  always  out  of  the  road 
requires  a  map  :  genuine  ignorance  occasionally  lapses  into  truth.  We 
thought  it  possible  M.  Libri  might  have  played  the  trick  to  show  how 
easily  the  French  are  deceived  ;  but  with  our  present  information,  our 
minds  are  at  rest  on  the  subject.  We  see  M.  Chasles  does  not  like  to 
avow  the  real  source  of  information :  lie  will  not  confess  himself  a 
spiritualist. 


30  A  BUDGET  OF  PARADOXES. 

Philo  of  Gradara  is  asserted  by  Montucla,  on  the  authority  of 
Eutocius,  the  commentator  on  Archimedes,  to  have  squared  the 
circle  within  the  ten-thousandth  part  of  a  unit,  that  is,  to  four 
places  of  decimals.  A  modern  classical  dictionary  represents  it  as 
done  by  Philo  to  ten  thousand  places  of  decimals.  Lacroix  com- 
ments on  Montucla  to  the  effect  that  myriad  (in  Greek  ten  thou- 
sand] is  here  used  as  we  use  it,  vaguely,  for  an  immense  number. 
On  looking  into  Eutocius,  I  find  that  not  one  definite  word  is 
said  about  the  extent  to  which  Philo  carried  the  matter.  I  give 
a  translation  of  the  passage  : — 

We  ought  to  know  that  Apollonius  Pergseus,  in  his  Ocytocium  [this 
work  is  lost],  demonstrated  the  same  by  other  numbers,  and  came 
nearer,  which  seems  more  accurate,  but  has  nothing  to  do  with 
Archimedes ;  for,  as  before  said,  he  aimed  only  at  going  near  enough 
for  the  wants  of  life.  Neither  is  Porus  of  Nicaea  fair  when  he  takes 
Archimedes  to  task  for  not  giving  a  line  accurately  equal  to  the 
circumference.  He  says  in  his  Cerii  that  his  teacher,  Philo  of  Gadara, 
had  given  a  more  accurate  approximation  (etc  tucpifiemipove  opiflyuovg 
ayayetv)  than  that  of  Archimedes,  or  than  7  to  22.  But  all  these  [the 
rest  as  well  as  Philo]  miss  the  intention.  They  multiply  and  divide  by 
tens  of  thousands,  which  no  one  can  easily  do,  unless  he  be  versed  in 
the  logistics  [fractional  computation]  of  Magnus  [now  unknown]. 

Montucla,  or  his  source,  ought  not  to  have  made  this  mistake. 
He  had  been  at  the  Greek  to  correct  Philo  Gadetanus,  as  he  had 
often  been  called,  and  he  had  brought  away  and  quoted  airo 
TaSapwv.  Had  he  read  two  sentences  further,  he  would  have 
found  the  mistake. 

We  here  detect  a  person  quite  unnoticed  hitherto  by  the 
moderns,  Magnus  the  arithmetician.  The  phrase  is  ironical ;  it 
is  as  if  we  should  say, '  To  do  this  a  man  must  be  deep  in  Cocker.' 
Accordingly,  Magnus,  Baveme,  and  Cocker,  are  three  personifica- 
tions of  arithmetic ;  and  there  may  be  more. 

Aristotle,  treating  of  the  category  of  relation,  denies  that  the 
quadrature  has  been  found,  but  appears  to  assume  that  it  can  be 
done.  Boethius,  in  his  comment  on  the  passage,  says  that  it  has 
been  done  since  Aristotle,  but  that  the  demonstration  is  too  long 
for  him  to  give.  Those  who  have  no  notion  of  the  quadrature 
question  may  look  at  the  English  Cyclopaedia,  art.  'Quadrature 
of  the  Circle.' 


EAKLY  CIRCLE  SQUARERS.  31 


Tetragonismus.  Id  est  circuli  quadratura  per  Campanula, 
Archimedem  Syracusanum,  atque  Boetium  mathematicse  per- 
spicacissimos  adinventa. — At  the  end,  Impressum  Venetiis  per 
loan.  Bapti.  Sessa.  Anno  ab  incarnatione  Domini,  1503.  Die 
28  Augusti. 

This  book  has  never  been  noticed  in  the  history  of  the  subject, 
and  I  cannot  find  any  mention  of  it.  The  quadrature  of  Campanus 
takes  the  ratio  of  Archimedes,  7  to  22,  to  be  absolutely  correct ; 
the  account  given  of  Archimedes  is  not  a  translation  of  his  book  ; 
and  that  of  Boetius  has  more  than  is  in  BoetAius.  This  book 
must  stand,  with  the  next,  as  the  earliest  in  print  on  the  subject, 
until  further  showing :  Murhard  and  Kastner  have  nothing  so 
early.  It  is  edited  by  Lucas  Gauricus,  who  has  given  a  short 
preface.  Luca  Gaurico,  Bishop  of  Civita  Ducale,  an  astrologer 
of  astrologers,  published  this  work  at  about  thirty  years  of  age, 
and  lived  to  eighty-two.  His  works  are  collected  in  folios,  but  I 
do  not  know  whether  they  contain  this  production.  The  poor  fellow 
could  never  tell  his  own  fortune,  because  his  father  neglected  to 
note  the  hour  and  minute  of  his  birth.  But  if  there  had  been 
anything  in  astrology,  he  could  have  worked  back,  as  Adams  and 
Leverrier  did  when  they  caught  Neptune  :  at  sixty  he  could  have 
examined  every  minute  of  his  day  of  birth,  by  the  events  of  his 
life,  and  so  would  have  found  the  right  minute.  He  could  then 
have  gone  on,  by  rules  of  prophecy.  Gauricus  was  the  mathe- 
matical teacher  of  Joseph  Scaliger,  who  did  him  no  credit,  as  we 
shall  see. 

In    hoc    opere   contenta  Epitome Liber    de    quadratura 

Circuli Paris,  1503,  folio. 

The  quadrator  is  Charles  Bovillus,  who  adopted  the  views  of 
Cardinal  Cusa,  presently  mentioned.  Montucla  is  hard  on  his 
compatriot,  who,  he  says,  was  only  saved  from  the  laughter  of 
geometers  by  his  obscurity.  Persons  must  guard  against  most 
historians  of  mathematics  in  one  point :  they  frequently  attribute 
to  Jns  oivn  age  the  obscurity  which  a  writer  has  in  their  own  time. 
This  tract  was  printed  by  Henry  Stephens,  at  the  instigation  of 
Faber  Stapulensis,  and  is  recorded  by  Dechales,  &c.  It  was  also 
introduced  into  the  'Margarita  Philosophica'  of  1815,  in  the 
same  appendix  with  the  new  perspective  from  Viator.  This  is  not 
extreme  obscurity,  by  any  means.  The  quadrature  deserved  it ; 
but  that  is  another  point. 


32  A   BUDGET   OF   PARADOXES. 

It  is  stated  by  Montucla  that  Bovillus  makes  TT  —  VW.  But 
Montucla  cites  a  work  of  1507,  Introductorium  Geometricum., 
which  I  have  never  seen.  He  finds  in  it  an  account  which 
Bovillus  gives  of  the  quadrature  of  the  peasant  labourer,  and 
describes  it  as  agreeing  with  his  own.  But  the  description  makes 
TT  =  3£,  which  it  thus  appears  Bovillus  could  not  distinguish 
from  V 10.  It  seems  also  that  this  3£,  about  which  we  shall  see 
so  much  in  the  sequel,  takes  its  rise  in  the  thoughtful  head  of  a 
poor  labourer.  It  does  him  great  honour,  being  so  near  the  truth, 
and  he  having  no  means  of  instruction.  In  our  day,  when  an 
ignorant  person  chooses  to  bring  his  fancy  forward  in  opposition 
to  demonstration  which  he  will  not  study,  he  is  deservedly 
laughed  at. 

Mr.  James  Smith,  of  Liverpool — hereinafter  notorified — attri- 
butes the  first  announcement  of  3^  to  M.  Joseph  Lacornme,  a 
French  well-sinker,  of  whom  he  gives  the  following  account  :— 

In  the  year  1836,  at  which  time  Lacomme  could  neither  read  nor 
write,  he  had  constructed  a  circular  reservoir  and  wished  to  know  the 
quantity  of  stone  that  would  be  required  to  pave  the  bottom,  and  for 
this  purpose  called  on  a  professor  of  mathematics.  On  putting  his 
question  and  giving  the  diameter,  he  was  surprised  at  getting  the 
following  answer  from  the  Professor — '  Qu'il  lui  e'ait  impossible  de  le  lid 
dire  au  juste,  attendu  quepersonne  n'avait  encore  pu  trouver  d'une  maniere 
exacte  le  rapport  de  la  circonference  au  diametre.'  From  this  he  was 
led  to  attempt  the  solution  of  the  problem.  His  first  process  was 
purely  mechanical,  and  he  was  so  far  convinced  he  had  made  the  dis- 
covery that  he  took  to  educating  himself,  and  became  an  expert 
arithmetician,  and  then  found  that  arithmetical  results  agreed  with  his 
mechanical  experiments.  He  appears  to  have  eked  out  a  bare  existence 
for  many  years  by  teaching  arithmetic,  all  the  time  struggling  to  get  a 
hearing  from  some  of  the  learned  societies,  but  without  success.  In 
the  year  1855  he  found  his  way  to  Paris,  where,  as  if  by  accident,  he 
made  the  acquaintance  of  a  young  gentleman,  son  of  M.  Winter,  a 
commissioner  of  police,  and  taught  him  his  peculiar  methods  of  calcu- 
lation. The  young  man  was  so  enchanted  that  he  strongly  recom- 
mended Lacomme  to  his  father,  and  subsequently  through  M.  Winter 
he  obtained  an  introduction  to  the  President  of  the  Society  of  Arts  and 
Sciences  of  Paris.  A  committee  of  the  society  was  appointed  to 
examine  and  report  upon  his  discovery,  and  the  society  at  its  seance 
of  March  17,  1856,  awarded  a  silver  medal  of  the  first  class  to 
M.  Joseph  Lacomme  for  his  discovery  of  the  true  ratio  of  diameter 
to  circumference  in  a  circle.  He  subsequently  received  three  other 
medals  from  other  societies.  While  writing  this  I  have  his  likeness 
before  me,  with  his  medals  on  his  breast,  which  stands  as  a  frontispiece 


NICHOLAS  OF  CUSA— AGRIPPA.  33 

to  a  short  biography  of  this  extraordinary  man,  for  which  I  am  in- 
debted to  the  gentleman  who  did  me  the  honour  to  publish  a  French 
translation  of  the  pamphlet  I  distributed  at  the  meeting  of  the  British 
Association  for  the  Advancement  of  Science,  at  Oxford,  in  1860. — 
Correspo-ndent,  May  3,  1866. 

My  inquiries  show  that  the  story  of  the  medals  is  not  incredible. 
There  are  at  Paris  little  private  societies  which  have  not  so  much 
claim  to  be  exponents  of  scientific  opinion  as  our  own  Mechanics' 
Institutes.  Some  of  them  were  intended  to  give  a  false  lustre :  as 
the  *  Institut  Historique,'  the  members  of  which  are  '  Membre  de 
1'Institut  Historique.'  That  M.  Lacomme  should  have  got  four 
medals  from  societies  of  tbis  class  is  very  possible  :  that  be  should 
have  received  one  from  any  society  at  Paris  wbicb  bas  tbe  least 
claim  to  give  one  is  as  yet  simply  incredible. 

Nicolai  de  Cusa  Opera  Omnia.     Venice,  1514.     3  vols.  folio. 

The  real  title  is  'Haec  accurata  recognitio  trium  voluminum 
operum  clariss.  P.  Nicolai  Cusse  .  ,  .  proximo  sequens  pagina 
monstrat.'  Cardinal  Cusa,  wbo  died  in  1464,  is  one  of  tbe  earliest 
modern  attempters.  His  quadrature  is  found  in  tbe  second 
volume,  and  is  now  quite  unreadable.  In  these  early  days  every 
quadrator  found  a  geometrical  opponent,  wbo  finished  him. 
Eegiomontanus  did  tbis  office  for  tbe  Cardinal. 

De  Occulta  Philosophia  libri  III.     By  Henry  Cornelius  Agrippa. 

Lyons,  1550,  8vo. 
De  incertitudine  et  vanitate  scientiarum.    By  the  same.     Cologne, 

1531,  8vo. 

Tbe  first  editions  of  these  works  were  of  1530,  as  well  as  I  can 
make  out;  but  tbe  first  was  in  progress  in  1510.     In  the  second 
work  Agrippa  repents  of  having  wasted  time  on  the  magic  of  tbe 
first ;  but  all  those  who  actually  deal  witb  demons  are  destined 
to  eternal  fire  witb  Jamnes  and  Mambres   and    Simon  Magus. 
This  means,  as  is  tbe  fact,  that  his  occult  philosophy  did  not  actu- 
ally enter  upon  black  magic,  but  confined  itself  to  the  power  of 
tbe  stars,  of  numbers,  &c.     The  fourth  book,  which  appeared  after 
tbe  deatb  of  Agrippa,  and  really  concerns  dealing  witb  evil  spirits, 
is  undoubtedly  spurious.     It  is  very  difficult  to  make  out  what 
Agrippa  really  believed  on  tbe  subject.     I  have  introduced  his 
books  as  the  most  marked  specimens  of  treatises  on  magic,  a 
paradox  of  our  day,  though  not  far  from  orthodoxy  in  bis ;    and 
bere  I  should  have  ended  my  notice,  if  I  had  not  casually  found 
something  more  interesting  to  tbe  reader  of  our  day. 

D 


34  A  BUDGET   OF  PARADOXES. 

Walter  Scott,  it  is  well  known,  was  curious  on  all  matters 
connected  with  magic,  and  has  used  them  very  widely.  But  it  is 
hardly  known  how  much  pains  he  has  taken  to  be  correct,  and  to 
give  the  real  thing.  The  most  decided  detail  of  a  magical  pro- 
cess which  is  found  in  his  writings  is  that  of  Dousterswivel  in 
'  The  Antiquary  ' ;  and  it  is  obvious,  by  his  accuracy  of  process, 
that  he  does  not  intend  the  adept  for  a  mere  impostor,  but  for 
one  who  had  a  lurking  belief  in  the  efficacy  of  his  own  processes, 
coupled  with  intent  to  make  a  fradulent  use  of  them.  The 
materials  for  the  process  are  taken  from  Agrippa.  I  first  quote 
Mr.  Dousterswivel : 

...  I  take  a  silver  plate  when  she  [the  moon]  is  in  her  fifteenth 
mansion,  which  mansion  is  in  de  head  of  Libra,  and  I  engrave  upon  one 
side  de  worts  Schedbarschemoth  Schartachan  \_ch  should  be  t~\ — dat  is, 
de  Intelligence  of  de  Intelligence  of  de  moon — and  I  make  his  picture 
like  a  flying  serpent  with  a  turkey-cock's  head — vary  well — Then  upon 
this  side  I  make  de  table  of  de  moon,  which  is  a  square  of  nine, 
multiplied  into  itself,  with  eighty-one  numbers  [nine]  on  every  side, 
and  diameter  nine.  .  .  . 

In  the'De  Occulta  Philosophia,'  p.  290,  we  find  that  the 
fifteenth  mansion  of  the  moon  incipit  capite  Librae,  and  is  good 
pro  extrahendis  thesauris,  the  object  being  to  discover  hidden 
treasure.  In  p.  246,  we  learn  that  a  silver  plate  must  be  used 
with  the  moon.  In  p.  248,  we  have  the  words  which  denote  the 
Intelligence,  &c.  But,  owing  to  the  falling  of  a  number  into  a 
wrong  line,  or  the  misplacement  of  a  line,  one  or  other — which 
takes  place  in  all  the  editions  I  have  examined — Scott  has,  sad 
to  say,  got  hold  of  the  wrong  words  ;  he  has  written  down  the 
demon  of  the  demons  of  the  moon.  Instead  of  the  gibberish 
above,  it  should  have  been  Malcha  betharsisim  hed  beruah  sche- 
hakim.  In  p.  253,  we  have  the  magic  square  of  the  moon,  with 
eighty-one  numbers,  and  the  symbol  for  the  Intelligence,  which 
Scott  likens  to  a  flying  serpent  with  a  turkey-cock's  head.  He 
was  obliged  to  say  something ;  but  I  will  stake  my  character — 
and  so  save  a  woodcut — on  the  scratches  being  more  like  a  pair 
of  legs,  one  shorter  than  the  other,  without  a  body,  jumping  over 
a  six-barred  gate  placed  side  uppermost.  Those  who  thought 
that  Scott  forged  his  own  nonsense,  will  henceforth  stand  corrected. 
As  to  the  spirit  Peolphan,  &c.,  no  doubt  Scott  got  it  from  the 
authors  he  elsewhere  mentions,  Nicolaus  Remigius  and  Petrus 
Thyracus  ;  but  this  last  word  should  be  Thyraeus. 

The  tendency  of  Scott's  mind  towards  prophecy  is  very  marked, 


OEONTIUS   FINAEUS-URSUS.  35 

and  it  is  always  fulfilled.  Hyder,  in  his  disguise,  calls  out  to 
Tippoo — '  Cursed  is  the  prince  who  barters  justice  for  lust ;  he 
shall  die  in  the  gate  by  the  sword  of  the  stranger.'  Tippoo  was 
killed  in  a  gateway  at  Seringapatam. 

Orontii  Finaei.  .   .  Quadrature  Circuli.     Paris,  1544,  4to. 

Orontius  squared  the  circle  out  of  all  comprehension ;  but  he 
was  killed  by  a  feather  from  his  own  wing.  His  former  pupil, 
John  Buteo,  the  same  who — I  believe  for  the  first  time — calculated 
the  question  of  Noah's  ark,  as  to  its  power  to  hold  all  the  animals 
and  stores,  unsquared  him  completely.  Orontius  was  the  author 
of  very  many  works,  and  died  in  1555.  Among  the  laudatory 
verses  which,  as  was  usual,  precede  this  work,  there  is  one  of  a 
rare  character  :  a  congratulatory  ode  to  the  wife  of  the  author. 
The  French  now  call  this  writer  Oronce  Finee  ;  but  there  is  much 
difficulty  about  delatinisation.  Is  this  more  correct  than  Oronce 
Fine,  which  the  translator  of  De  Thou  uses  ?  Or  than  Horonce 
Phine,  which  older  writers  give  ?  I  cannot  understand  why  M. 
de  Viette  should  be  called  Viete,  because  his  Latin  name  is  Vieta. 
It  is  difficult  to  restore  Buteo  ;  for  not  only  now  is  butor  a  block- 
head as  well  as  a  bird,  but  we  really  cannot  know  what  kind  of 
bird  Buteo  stood  for.  We  may  be  sure  that  Madame  Fine  was 
Denise  Blanche  ;  for  Dionysia  Candida  can  mean  nothing  else. 
Let  her  shade  rejoice  in  the  fame  which  Hubertus  Sussannaeus 
has  given  her. 

I  ought  to  add  that  the  quadrature  of  Orontius,  and  solutions 
of  all  the  other  difficulties,  were  first  published  in  *  De  Kebus 
Mathematicis  Hactenus  Desideratis,'  of  which  I  have  not  the  date. 

Nicolai  Baymari  Ursi  Dithmarsi  Fundamentum  Astronomicum, 
id  est,  nova  doctrina  sinuum  et  triangulorum.  .  .  .  Strasburg, 
1588,  4to. 

People  choose  the  name  of  this  astronomer  for  themselves :  I 
take  Ursus,  because  he  was  a  bear.  This  book  gave  the  quadra- 
ture of  Simon  Duchesne,  or  a  Quercu,  which  excited  Peter  Metius, 
as  presently  noticed.  It  also  gave  that  unintelligible  reference  to 
Justus  Byrgius  which  has  been  used  in  the  discussion  about  the 
invention  of  logarithms. 

The  real  name  of  Duchesne  is  Van  der  Eycke.  I  have  met 
with  a  tract  in  Dutch,  Letterkundige  Aanteekeningen,  upon  Van 
Eycke,  Van  Ceulen,  &c.,  by  J.  J.  Dodt  van  Flensburg,  which  I 
make  out  to  be  since  1841  in  date.  I  should  much  like  a  trans- 

»  2 


36  A   BUDGET   OF  PARADOXES. 

lation  of  this  tract  to  be  printed,  say  in  the  Phil.  Mag.  Dutch 
would  be  clear  English  if  it  were  properly  spelt.  For  example, 
learn-master  would  be  seen  at  once  to  be  teacher ;  but  they  will 
spell  it  leermeester.  Of  these  they  write  as  van  deze;  widow 
they  make  weduwe.  All  this  is  plain  to  me,  who  never  saw  a 
Dutch  dictionary  in  my  life ;  but  many  of  their  mispellings  are 
quite  unconquerable. 

Jacobus  Falco  Valentinus,  miles  Ordinis  Montesiani,  hanc  circuli 
quadraturam  invenit.     Antwerp,  1589,  4to. 

The  attempt  is  more  than  commonly  worthless ;  but  as  Mon- 
tucla  and  others  have  referred  to  the  verses  at  the  end,  and  as  the 
tract  is  of  the  rarest,  I  will  quote  them  : — 

Circulus  loquitur. 

Vocabar  ante  circulus 
Eramque  curvus  undique 
Ut  alta  solis  orbita 
Et  arcus  ille  nubium. 
Eram  figura  nobilis 
Carensque  sola  origine 
Carensque  sola  termino. 
Modo  indecora  prodeo 
Novisque  foedor  angulis. 
Nee  hoc  peregit  Archytas 
Neque  Icari  pater  neque 
THUS  lapete  filius. 
Quis  ergo  casus  aut  Deus 
Meam  quadravit  aream  ? 

Hespondet  auctor. 

Ad  alta  Turiee  ostia 
Lacumque  limpidissimum 
Sita  est  beata  ci vitas 
Parum  Saguntus  abfuit 
Abestque  Sucro  plusculum. 
Hie  est  poeta  quispiam 
Libenter  astra  consulens 
Sibique  semper  arrogans 
Negata  doctioribus. 
Senex  ubique  cogitans 
Sui  frequenter  immemor 
Nee  explicare  circinum 


PETER   BUNGUS.  37 

Nee  exarare  lineas 
Sciens  ut  ipse  praedicat. 
Hie  ergo  bellus  artifex 
Tuam  quadra vit  aream. 

Falco's  verses  are  pretty,  if  the  w  ~  mysteries  be  correct ;  but  of 
these  things  I  have  forgotten — what  I  knew.  [One  mistake  has 
been  pointed  out  to  me  :  it  is  Archytas]. 

As  a  specimen  of  the  way  in  which  history  is  written,  I  copy 
the  account  which  Montucla — who  is  accurate  when  he  writes 
about  what  he  has  seen — gives  of  these  verses.  He  gives  the  date 
1587  ;  he  places  the  verses  at  the  beginning  instead  of  the  end; 
he  says  the  circle  thanks  its  quadrator  affectionately ;  and  he 
says  the  good  and  modest  chevalier  gives  all  the  glory  to  the 
patron  saint  of  his  order.  All  of  little  consequence,  as  it  happens ; 
but  writing  at  second-hand  makes  as  complete  mistakes  about 
more  important  matters. 

Petri  Biingi  Bergomatis  Numeronim  mysteria.      Bergomi  [Ber- 
gamo], 1591,  4to.     Second  Edition. 

The  first  edition  is  said  to  be  of  1585  ;  the  third,  Paris,  1618. 
Bungus  is  not  for  my  purpose  on  his  own  score,  but  those  who 
gave  the  numbers  their  mysterious  characters :  he  is  but  a  collector. 
He  quotes  or  uses  402  authors,  as  we  are  informed  by  his  list : 
this  just  beats  Warburton,  whom  some  eulogist  or  satirist,  I  forget 
which,  holds  up  as  having  used  400  authors  in  some  one  work. 
Bungus  goes  through  1,  2,  3,  &c.,  and  gives  the  account  of  every- 
thing remarkable  in  which  each  number  occurs ;  his  accounts  not 
being  always  mysterious.  The  numbers  which  have  nothing  to 
say  for  themselves  are  omitted :  thus  there  is  a  gap  between  50 
and  60.  In  treating  666,  Bungus,  a  good  Catholic,  could  not 
compliment  the  Pope  with  it,  but  he  fixes  it  on  Martin  Luther 
with  a  little  forcing.  If  from  A  to  I  represent  1-10,  from  K  to 
S  10-90,  and  from  T  to  Z  100-500,  we  see— 

MARTIN         LU      TERA 

30  1  80  100  9  40        20  200  100  5  80    1 

which  gives  666.     Again,  in  Hebrew,  Lulter  does  the  same : — 

i     n     h    1    *> 
200  400  30  6  30 

And  thus  two  can  play  at  any  game.  The  second  is  better 
than  the  first :  to  Latinise  the  surname  and  not  the  Christian 
name  is  very  unscholarlike.  The  last  number  mentioned  is  a 


38  A   BUDGET   OF   PARADOXES. 

thousand  millions ;  all  greater  numbers  are  dismissed  in  half  a 
page.  Then  follows  an  accurate  distinction  between  number 
and  multitude — a  thing  much  wanted  both  in  arithmetic  and 
logic. 

What  may  be  the  use  of  such  a  book  as  this  ?     The  last  occa- 
sion on  which  it  was  used  was  the  following.     Fifteen  or  sixteen 
years  ago  the  Koyal  Society  determined  to  restrict  the  number  of 
yearly  admissions  to  fifteen  men  of  science,  and  noblemen  ad 
libitum ;  the  men  of  science  being  selected  and  recommended  by 
the  Council,  with  a  power,  since  practically  surrendered,  to  the 
Society  to  elect  more.     This  plan  appears  to  me  to  be  directly 
against  the  spirit  of  their  charter,  the  true  intent  of  which  is, 
that  all  who  are  fit  should  be  allowed  to  promote  natural  know- 
ledge in  association,  from  and  after  the  time  at  which  they  are 
both  fit  and  willing.     It  is  also  working  more  absurdly  from  year 
to  year ;  the  tariff  of  fifteen  per  annum  will  soon  amoirnt  to  the 
practical  exclusion  of  many  who  would  be  very  useful.     This 
begins  to  be  felt  already,  I  suspect.     But,  as  appears  above,  the 
body  of  the  Society  has  the  remedy  in  its  own  hands.     When  the 
alteration  was  discussed  by  the  Council,  my  friend  the  late  Mr. 
Gralloway,  then  one  of   the  body,  opposed   it  strongly,  and  in- 
quired particularly  into  the  reason  why  fifteen,  of  all  numbers, 
was  the  one  to  be  selected.     Was  it  because  fifteen  is  seven  and 
eight,  typifying  the  Old  Testament  Sabbath,  and  the  New  Testa- 
ment day  of  the  resurrection  following  ?     Was  it  because  Paul 
strove  fifteen  days  against  Peter,  proving  that  he  was  a  doctor 
both  of  the  Old  and  New  Testament  ?     Was  it  because  the  prophet 
Hosea  bought  a  lady  for  fifteen  pieces  of  silver  ?     Was  it  because, 
according  to  Micah,  seven  shepherds   and   eight    chiefs  should 
waste  the  Assyrians?      Was  it  because  Ecclesiastes   commands 
equal  reverence  to  be  given  to  both  Testaments — such  was  the 
interpretation — in  the  words  '  Give  a  portion  to  seven,  and  also 
to  eight '  ?     Was  it  because  the  waters  of  the  Deluge  rose  fifteen 
cubits  above    the    mountains  ? — or  because   they   lasted   fifteen 
decades  of  days  ?     Was  it  because  Ezekiel's  temple  had  fifteen 
steps  ?     Was  it  because  Jacob's  ladder  has  been  supposed  to  have 
had  fifteen  steps  ?     Was  it  because  fifteen  years  were  added  to 
the  life  of  Hezekiah  ?     Was  it  because  the  feast  of  unleavened 
bread  was  on  the  fifteenth  day  of  the  month  ?     Was  it  because 
the  scene  of  the  Ascension  was  fifteen  stadia  from  Jerusalem  ? 
Was   it   because   the    stone-masons    and    porters    employed    in 
Solomon's  temple  amounted  to  fifteen  myriads  ?  &c.     The  Council 
were  amused  and  astounded  by  the  volley  of  fifteens  which  was 


THE   FIFTEENS   OF   BUNGUS.  39 

fired  at  them ;  they  knowing  nothing  about  Bungus,  of  which 
Mr.  Gralloway — who  did  not,  as  the  French  say,  indicate  his 
sources — possessed  the  copy  now  before  me.  In  giving  this 
anecdote  I  give  a  specimen  of  the  book,  which  is  exceedingly  rare. 
Should  another  edition  ever  appear,  which  is  not  very  probable, 
he  would  be  but  a  bungling  Bungus  who  should  forget  the  fifteen 
of  the  Royal  Society. 

[I  make  a  remark  on  the  different  colours  which  the  same 
person  gives  to  one  story,  according  to  the  bias  under  which  he 
tells  it.  My  friend  Galloway  told  me  how  he  had  quizzed  the 
Council  of  the  Royal  Society,  to  my  great  amusement.  When- 
ever I  am  struck  by  the  words  of  any  one,  I  carry  away  a  vivid 
recollection  of  position,  gestures,  tones,  &c.  I  do  not  know 
whether  this  be  common  or  uncommon.  I  never  recall  this  joke 
without  seeing  before  me  my  friend,  leaning  against  his  book- 
case, with  Bungus  open  in  his  hand,  and  a  certain  half-deprecia- 
tory tone  which  he  often  used  when  speaking  of  himself.  Long 
after  his  death,  an  F.E.S.  who  was  present  at  the  discussion,  told 
me  the  story.  I  did  not  say  I  had  heard  it,  but  I  watched  him, 
with  Gralloway  at  the  bookcase  before  me.  I  wanted  to  see 
whether  the  two  would  agree  as  to  the  fact  of  an  enormous 
budget  of  fifteens  having  been  fired  at  the  Council,  and  they 
did  agree  perfectly.  But  when  the  paragraph  of  the  Budget 
appeared  in  the  Athenaeum,  my  friend,  who  seemed  rather  to 
object  to  the  shewing-up,  assured  me  that  the  thing  was  grossly 
exaggerated  ;  there  was  indeed  a  fifteen  or  two,  but  nothing  like 
the  number  I  had  given.  I  had,  however,  taken  sharp  note  of 
the  previous  narration. 

I  will  give  another  instance.  An  Indian  officer  gave  me  an 
account  of  an  elephant,  as  follows.  A  detachment  was  on  the 
march,  and  one  of  the  gun-carriages  got  a  wheel  off  the  track, 
so  that  it  was  also  off  the  ground,  and  hanging  over  a  precipice. 
If  the  bullocks  had  moved  a  step,  carriages,  bullocks,  and  all 
must  have  been  precipitated.  No  one  knew  what  could  be  done 
until  some  one  proposed  to  bring  up  an  elephant,  and  let  him 
manage  it  his  own  way.  The  elephant  took  a  moment's  survey  of 
the  fix,  put  his  trunk  under  the  axle  of  the  free  wheel,  and  waited. 
The  surrounders,  who  saw  what  he  meant,  moved  the  bullocks 
gently  forward,  the  elephant  followed,  supporting  the  axle,  until 
there  was  ground  under  the  wheel,  when  he  let  it  quietly  down. 
From  all  I  had  heard  of  the  elephant,  this  was  not  too  much 
to  believe.  But  when,  years  afterwards,  I  reminded  my  friend 


40  A   BUDGET   OF  PARADOXES. 

of  his  story,  he  assured  me  that  I  had  misunderstood  him,  that 
the  elephant  was  directed  to  put  his  trunk  under  the  wheel,  and 
saw  in  a  moment  why.  This  is  reasonable  sagacity,  and  very 
likely  the  correct  account ;  but  I  am  quite  sure  that,  in  the  fit 
of  elephant-worship  under  which  the  story  was  first  told,  it  was 
told  as  I  have  first  stated  it.] 

[Jordani  Bruni  Nolani  de  Monade,  Numero  et  Figura  .  .  .  item  de 
Innumerabilibus,  Immense,  et  Infigurabili.  .  .  Frankfort,  1591, 
8vo. 

I  cannot  imagine  how  I  came  to  omit  a  writer  whom  I  have 
known  so  many  years,  unless  the  following  story  will  explain  it. 
The  officer  reproved  the  boatswain  for  perpetual  swearing ;  the 
boatswain  answered  that  he  heard  the  officers  swear.  '  Only  in 
an  emergency,'  said  the  officer.  'That's  just  it,'  replied  the 
other ;  '  a  boatswain's  life  is  a  life  of  'mergency.'  OKordano 
Bruno  was  all  paradox ;  and  my  mind  was  not  alive  to  his 
paradoxes,  just  as  my  ears  might  have  become  dead  to  the  boat- 
swain's oaths.  He  was,  as  has  been  said,  a  vorticist  before 
Descartes,  an  optimist  before  Leibnitz,  a  Copernican  before 
Gralileo.  It  would  be  easy  to  collect  a  hundred  strange  opinions 
of  his.  He  was  born  about  1550,  and  was  roasted  alive  at  Rome, 
February  17,  1600,  for  the  maintenance  and  defence  of  the  holy 
Church,  and  the  rights  and  liberties  of  the  same.  These  last 
words  are  from  the  writ  of  our  own  good  James  I.,  under  which 
Leggatt  was  roasted  at  Smithfield,  in  March  1612 ;  and  if  I  had  a 
.copy  of  the  instrument  under  which  Wightman  was  roasted  at 
Litchfield,  a  month  afterwards,  I  daresay  I  should  find  something 
quite  as  edifying.  1  extract  an  account  which  I  gave  of  Bruno 
in  the  Comp.  Aim.  for  1855  : — 

He  was  first  a  Dominican  priest,  then  a  Calvinist ;  and  was  roasted 
alive  "at  Rome,  in  1600,  for  as  many  heresies  of  opinion,  religious  and 
philosophical,  as  ever  lit  one  fire.  Some  defenders  of  the  papal  cause 
Lave  at  least  worded  their  accusations  so  to  be  understood  as  imputing 
to  him  villainous  actions.  But  it  is  positively  certain  that  his  death 
was  due  to  opinions  alone,  and  that  retractation,  even  after  sentence, 
would  have  saved  him.  There  exists  a  remarkable  letter,  written  from 
Home  on  the  very  clay  of  the  murder,  by  Scioppius  (the  celebrated 
scholar,  a  waspish  convert  from  Lutheranism,  known  by  his  hatred  to 
Protestants  and  Jesuits)  to  Rittershusius,  a  well-known  Lutheran 
writer  on  civil  and  cation  law,  whose  works  are  in  the  index  of  prohi- 
bited books.  This  letter  has  been  reprinted  by  Libri  (vol.  iv.  p.  407). 
The  writer  informs  his  friend  (whom  he  wished  to  convince  that  even  a 
Lutheran  would  have  burnt  Bruno)  that  all  Rome  would  tell  him  that 


GIOKDANO   BBUNO.  41 

Bruno  died  for  Lutheranism ;  but  this  is  because  the  Italians  do  not 
know  the  difference  between  one  heresy  and  another,  in  which  simpli- 
city (says  the  writei*)  may  God  preserve  them.  That  is  to  say,  they 
knew  the  difference  between  a  live  heretic  and  a  roasted  one  by  actual 
inspection,  but  had  no  idea  of  the  difference  between  a  Lutheran  and  a 
Calvinist.  The  countrymen  of  Boccaccio  would  have  smiled  at  the  idea 
which  the  German  scholar  entertained  of  them.  They  said  Bruno  was 
burnt  for  Lutheranism,  a  name  under  which  they  classed  all  Protestants : 
and  they  are  better  witnesses  than  Schopp,  or  Scioppius.  He  then 
proceeds  to  describe  to  big  Protestant  friend  (to  whom  he  would 
certainly  not  have  omitted  any  act  which  both  their  Churches  would 
have  condemned)  the  mass  of  opinions  with  which  Bruno  was  charged  ; 
as  that  there  are  innumerable  worlds,  that  souls  migrate,  that  Moses 
was  a  magician,  that  the  Scriptures  are  a  dream,  that  only  the  Hebrews 
descended  from  Adam  and  Eve,  that  the  devils  would  be  saved,  that 
Christ  was  a  magician  and  deservedly  put  to  death,  &c.  In  fact,  says 
he,  Bruno  has  advanced  all  that  was  ever  brought  forward  by  all 
heathen  philosophers,  and  by  all  heretics,  ancient  and  modern.  A  time 
for  retractation  was  given,  both  before  sentence  and  after,  which  should 
be  noted,  as  well  for  the  wretched  palliation  which  it  may  afford,  as  for 
the  additional  proof  it  gives  that  opinions,  and  opinions  only,  brought 
him  to  the  stake.  In  this  medley  of  charges  the  Scriptures  are  a  dream, 
while  Adam,  Eve,  devils,  and  salvation  are  truths,  and  the  Saviour  a 
deceiver.  We  have  examined  no  work  of  Bruno  except  the  De  Monade, 
8fc.,  mentioned  in  the  text.  A  strong  though  strange  theism  runs 
through  the  whole,  and  Moses,  Christ,  the  Fathers,  &c.,  are  cited  in  a 
manner  which  excites  no  remark  either  way.  Among  the  versions  of 
the  cause  of  Bruno's  death  is  atheism :  but  this  word  was  very  often 
used  to  denote  rejection  of  revelation,  not  merely  in  the  common  course 
of  dispute,  but  by  such  writers,  for  instance,  as  Brucker  and  Morhof. 
Thus  Morhof  says  of  the  De  Monade,  8fc.,  that  it  exhibits  no  manifest 
signs  of  atheism.  What  he  means  by  the  word  is  clear  enough,  when 
he  thus  speaks  of  a  work  which  acknowledges  God  in  hundreds  of 
places,  and  rejects  opinions  as  blasphemous  in  several.  The  work  of 
Bruno  in  which  his  astronomical  opinions  are  contained  is  De  Monade, 
8fc.  (Frankfort,  1591,  8vo).  He  is  the  most  thorough-going  Copernican 
possible,  and  throws  out  almost  every  opinion,  true  or  false,  which  has 
ever  been  discussed  by  astronomers,  from  the  theory  of  innumerable 
inhabited  worlds  and  systems  to  that  of  the  planetary  nature  of  comets. 
Libri  (vol.  iv.)  has  reprinted  the  most  striking  part  of  his  expressions 
of  Coperuican  opinion. 

The  Satanic  doctrine  that  a  Church  may  employ  force  in  aid 
of  its  dogma  is  supposed  to  be  obsolete  in  England,  except  as  an 
individual  paradox ;  but  this  is  difficult  to  settle.  Opinions 
are  much  divided  as  to  what  the  Roman  Church  would  do  in 


42  A  BUDGET   OE  PAKADOXES. 

England,  if  she  could :  any  one  who  doubts  that  she  claims  the 
right    does   not  deserve    an   answer.      When   the  hopes  of  the 
Tractarian  section  of  the  High  Church  were  in  bloom,  before  the 
most  conspicuous  intellects  among  them  had  transgressed  their 
ministry,  that  they  might  goto  their  own  place,  I  had  the  curiosity 
to  see  how  far  it  could  be  ascertained  whether  they  held  the 
only  doctrine  which  makes  me  the  personal  enemy  of  a  sect.     I 
found  in  one  of  their  tracts  the  assumption  of  a  right  to  per- 
secute,  modified  by  an  asserted  conviction  that  force  was  not 
efficient.      I   cannot  now   say   that   this  tract  was   one   of  the 
celebrated  ninety  ;  and  on  looking  at  the  collection  I  find  it  so 
poorly  furnished  with  contents,  &c.,  that  nothing  but  searching 
through  three  thick  volumes  would  decide.     In  these  volumes  I 
find,  augmenting  as  we  go  on,  declarations  about  the  character 
and  power  of  '  the  Church '  which  have  a  suspicious  appearance. 
The  suspicion  is   increased  by  that  curious  piece   of  sophistry, 
No.  87,  on  religious  reserve.     The  queer  paradoxes  of  that  tract 
leave  iis  in  doubt  as  to  everything  but  t^his,  that  the  church(man) 
is  not  bound  to  give  his  whole  counsel  in  all   things,  and  not 
bound  to  say  what  the  things  are  in  which  he  does  not  give  it. 
It  is  likely  enough  that  some   of  the  '  rights  and  liberties '  are 
but  scantily  described.     There  is  now  no  fear ;  but  the  time  was 
when,  if  not  fear,  there  might  be  a  looking  for  of  fear  to  come ; 
nobody  could  then  be  so  sure  as  we  now  are  that  the  lion  was 
only  asleep.     There  was  every  appearance  of  a  harder  fight  at 
hand  than  was  really  found  needful. 

Among  other  exquisite  quirks  of  interpretation  in  the  No.  87 
above  mentioned  is  the  following.  GTod  himself  employs  re- 
serve ;  he  is  said  to  be  decked  with  light  as  with  a  garment  (the 
old  or  prayer-book  version  of  Psalm  civ.  2).  To  an  ordinary 
apprehension  this  would  be  a  strong  image  of  display,  manifesta- 
tion, revelation ;  but  there  is  something  more.  '  Does  not  a 
garment  veil  in  some  measure  that  which  it  clothes  ?  Is  not 
that  very  light  concealment  ?  ' 

This  No.  87,  admitted  into  a  series,  fixes  upon  the  managers 
of  the  series,  who  permitted  its  introduction,  a  strong  presump- 
tion of  that  underhand  intent  with  which  they  were  charged. 
At  the  same  time  it  is  honourable  to  our  liberty  that  this  series 
could  be  published :  though  its  promoters  were  greatly  shocked 
when  the  Essayists  and  Bishop  Colenso  took  a  swing  on  the 
other  side.  When  No.  90  was  under  discussion,  Dr.  Maitland, 
the  librarian  at  Lambeth,  asked  Archbishop  Howley  a  question 
about  No.  89.  *  I  did  not  so  much  as  know  there  was  a  No.  89^ 


RITUALISM.  I-! 

was  the  answer.  I  am  almost  sure  I  have  seen  this  in  print, 
and  quite  sure  that  Dr.  Maitland  told  it  to  me.  It  is  creditable 
that  there  was  so  much  freedom ;  but  No.  90  was  too  bad,  and 
was  stopped. 

The  Tractarian  mania  has  now  (October  1866)  settled  down 
into  a  chronic  vestment  disease,  complicated  with  fits  of  tran- 
substantiation,  which  has  taken  the  name  of  Ritualism.  The 
common  sense  of  "our  national  character  will  not  put  up  with  a 
continuance  of  this  grotesque  folly  ;  millinery  in  all  its  branches 
will  at  last  be  advertised  only  over  the  proper  shops.  I  am  told 
that  the  Eitualists  give  short  and  practical  sermons ;  if  so,  they 
may  do  good  in  the  end.  The  English  Establishment  has  always 
contained  those  who  want  an  excitement ;  the  New  Testament, 
in  its  plain  meaning,  can  do  little  for  them.  Since  the  Ee  volu- 
tion, Jacobitism,  Wesleyanism,  Evangelicism,  Puseyism,  and 
Eitualism,  have  come  on  in  turn,  and  have  furnished  hot  water 
for  those  who  could  not  wash  without  it.  If  the  Eitualists  should 
succeed  in  substituting  short  and  practical  teaching  for  the 
high-spiced  lectures  of  the  doctrinalists,  they  will  be  remembered 
with  praise.  John  the  Baptist  would  perhaps  not  have  brought 
all  Jerusalem  out  into  the  wilderness  by  his  plain  and  good 
sermons  :  it  was  the  camel's  hair  and  the  locusts  which  got  him 
a  congregation,  and  which,  perhaps,  added  force  to  his  precepts. 
When  at  school  I  heard  a  dialogue,  between  an  usher  and  the 

man  who  cleaned  the  shoes,  about  Mr. ,  a  minister,  a  very 

corporate  body  with  due  area  of  waistcoat.  '  He  is  a  man  of 
great  erudition,'  said  the  first.  '  Ah,  yes,  sir,'  said  Joe ;  '  any- 
one can  see  that  who  looks  at  that  silk  waistcoat.'] 

[When  I  said  at  the  outset  that  I  had  only  taken  books 
from  my  own  store,  I  should  have  added  that  I  did  not  make  any 
search  for  information  given  as  part  of  a  work.  Had  I  looked 
through  all  my  books,  I  might  have  made  some  curious  additions. 
For  instance,  in  Schott's  Magia  Naturalis  (vol.  iii.  pp.  756-778) 
is  an  account  of  the  quadrature  of  Gephyrauder,  as  he  is  mis- 
printed in  Montucla.  He  was  Thomas  Gephyrander  Salicetus; 
and  he  published  two  editions,  in  1608  and  1609 :  I  never  even 
heard  of  a  copy  of  either.  His  work  is  of  the  extreme  of  absurdity  : 
he  makes  a  distinction  between  geometrical  and  arithmetical  frac- 
tions, and  evolves  theorems  from  it.  More  curious  than  his  quad- 
rature is  his  name  ;  what  are  we  to  make  of  it  ?  If  a  German,  he  is 
probably  a  German  form  of  Bridgeman,  and  Salicetus  refers  him  to 
Weiden.  But  Thomas  was  hardly  a  German  Christian  name  of  his 


44  A   BUDGET   OF  PAEADOXES. 

time  ;  of  526  German  philosophers,  physicians,  lawyers,  and  theolo- 
gians who  were  biographed  by  Melchior  Adam,  only  two  are  of  this 
name.  Of  these  one  is  Thomas  Erastus,  the  physician  whose  theolo- 
gical writings  against  the  Church  as  a  separate  power  have  given  the 
name  of  Erastians  to  those  who  follow  his  doctrine,  whether  they 
have  heard  of  him  or  not.  Erastus  is  little  known ;  accordingly, 
some  have  supposed  that  he  must  be  Erastus,  the  friend  of  St. 
Paul  and  Timothy  (Acts  xix.  22 ;  2  Tim.  iv.  20  ;  Kom.  xvi.  23), 
but  what  this  gentleman  did  to  earn  the  character  is  not  hinted 
at.  P^ew  words  would  have  done  :  Grains  (Eom.  xvi.  23)  has  an 
immortality  which  many  more  noted  men  have  missed,  given  by 
John  Bunyan,  out  of  seven  words  of  St.  Paul.  I  was  once  told 
that  the  Erastians  got  their  name  from  Blastus,  and  I  could  not 
solve  bl  =  er :  at  last  I  remembered  that  Blastus  was  a  chamber- 
lain as  well  as  Erastus  ;  hence  the  association  which  caused  the 
mistake.  The  real  heresiarch  was  a  physician  who  died  in  1583  ; 
his  heresy  was  promulgated  in  a  work,  published  immediately 
after  his  death  by  his  widow,  De  Excommunicatione  Ecclesiastica. 
He  denied  the  power  of  excommunication  on  the  principle  above 
stated ;  and  was  answered  by  Beza.  The  work  was  translated  by 
Dr.  R.  Lee  (Edinb.  1844,  8vo).  The  other  is  Thomas  Grynseus, 
a  theologian,  nephew  of  Simon,  who  first  printed  Euclid  in  Greek ; 
of  him  Adam  says  that  of  works  he  published  none,  of  learned 
sons  four.  If  Gephyrander  were  a  Frenchman,  his  name  is  not  so 
easily  guessed  at ;  but  he  must  have  been  of  La  Saussaye.  The 
account  given  by  Schott  is  taken  from  a  certain  Father  Philip 
Colbinus,  who  wrote  against  him. 

In  some  manuscripts  lately  given  to  the  Eoyal  Society, 
David  Gregory,  who  seems  to  have  seen  Gephyrander's  work,  calls 
him  Salicetus  Westphalus,  which  is  probably  on  the  title-page. 
But  the  only  Weiden  I  can  find  is  in  Bavaria.  Murhard  has  both 
editions  in  his  Catalogue,  but  had  plainly  never  seen  the  books  : 
he  gives  the  author  as  Thomas  Gep.  Hyandrus,  Salicettus  West- 
phalus.  Murhard  •  is  a  very  old  referee  of  mine ;  but  who  the 
non  nominandus  was  to  see  Montucla's  Gephyrauder  in  Murhard's 
Gep.  Hyandrus,  both  writers  being  usually  accurate  ?] 


NAPIEK— GILBERT— BAPTIST  A  PORTA.  45 


A  plain  discoverie  of  the  whole  Revelation  of  St.  John  .  .  . 
whereunto  are  annexed  certain  oracles  of  Sibylla  .  .  .  Set  Foorth 
by  John  Napeir  L.  of  Marchiston.  London,  1611,  4to. 

The  first  edition  was  Edinburgh,  1593,  4to.  Napier  always 
believed  that  his  great  mission  was  to  upset  the  Pope,  and  that 
logarithms,  and  such  things,  were  merely  episodes  and  relaxations. 
It  is  a  pity  that  so  many  books  have  been  written  about  this 
matter,  while  Napier,  as  good  as  any,  is  forgotten  and  unread. 
He  is  one  of  the  first  who  gave  us  the  six  thousand  years.  '  There 
is  a  sentence  of  the  house  of  Elias  reserved  in  all  ages,  bearing 
these  words :  The  world  shall  stand  six  thousand  years,  and  then 
it  shall  be  consumed  by  fire  :  two  thousand  yeares  voide  or  without 
lawe,  two  thousand  yeares  under  the  law,  and  two  thousand 
yeares  shall  be  the  daies  of  the  Messias.  .  .  .' 

I  give  Napier's  parting  salute  :  it  is  a  killing  dilemma  : — 

In  summar  conclusion,  if  thou  o  Borne  aledges  thyselfe  reformed,  and 
to  beleeue  true  Christianisme,  then  beleeue  Saint  John  the  Disciple, 
whome  Christ  loued,  publikely  here  in  this  Reuelation  proclaiming  thy 
wracke,  but  if  thou  remain  Ethnick  in  thy  priuate  thoghts,  beleeuing 
the  old  Oracles  of  the  Sibyls  reuerently  keeped  somtime  in  thy  Capitol : 
then  doth  here  this  Sibyll  proclame  also  thy  wracke.  Repent  therefore 
alwayes,  in  this  thy  latter  breath,  as  thou  louest  thine  Eternall  salvation. 
Amen. 

— Strange  that  Napier  should  not  have  seen  that  this  appeal  could 
not  succeed,  unless  the  prophecies  of  the  Apocalypse  were  no  true 
prophecies  at  all. 

De  Magnete  magneticisque  corporibus,  et  de  magno  magnete 
tellure.  By  William  Gilbert.  London,  1600,  folio.— There  is 
a  second  edition  ;  and  a  third,  according  to  Watt. 

Of  the  great  work  on  the  magnet  there  is  no  need  to  speak, 
though  it  was  a  paradox  in  its  day.  The  posthumous  work  of 
Gilbert,  'De  Mundo  nostro  sublunari  philosophia  nova'  (Ams- 
terdam, 1651,  4to)  is,  as  the  title  indicates,  confined  to  the 
physics  of  the  globe  and  its  atmosphere.  It  has  never  excited 
attention :  I  should  hope  it  would  be  examined  with  our  present 
lights. 

Elementorum  Curvilineorium  Libri  tres.    By  John  Baptista  Porta. 

Rome,  1610,  4to. 

This  is  a  ridiculous  attempt,  which  defies  description,  except 
that  it  is  all  about  lunules.  Porta  was  a  voluminous  writer. 


46  A  BUDGET   OF  PARADOXES. 

His  printer  announces  fourteen  works  printed,  and  four  to  come, 
besides  thirteen  plays  printed,  and  eleven  waiting.  His  name  is, 
and  will  be,  current  in  treatises  on  physics  for  more  reasons  than 
one. 

Trattato  della  quadratura  del  cerchio.     Di  Pietro  Antonio  Cataldi. 
Bologna,  1612,  folio. 

Eheticus,  Vieta,  and  Cataldi  are  the  three  untiring  computers 
of  Germany,  France,  and  Italy ;  Napier  in  Scotland,  and  Briggs  in 
England,  come  just  after  them.  This  work  claims  a  place  as 
beginning  with  the  quadrature  of  Pellegrino  Borello  of  Reggio, 
who  will  have  the  circle  to  be  exactly  3  diameters  and  -^^  of  a 
diameter.  Cataldi,  taking  Van  Ceulen's  approximation,  works 
hard  at  the  finding  of  integers  which  nearly  represent  the  ratio. 
He  had  not  then  the  continued  fraction,  a  mode  of  representation 
which  he  gave  the  next  year  in  his  work  on  the  square  root.  He 
\has  but  twenty  of  Van  Ceulen's  thirty  places,  which  he  takes  from 
Clavius :  and  anyone  might  be  puzzled  to  know  whence  the  Italians 
got  the  result ;  Van  Ceulen,  in  1612,  not  having  been  translated 
from  Dutch.  But  Clavius  names  his  comrade  Grruenberger,  and 
attributes  the  approximation  to  them  jointly  ;  *  Lud.  a  Collen  et 
Chr.  Grruenbergerus  invenerunt,'  which  he  had  no  right  to  do, 
unless,  to  his  private  knowledge,  Grruenberger  had  verified  Van 
Ceulen.  And  Grruenberger  only  handed  over  twenty  of  the  places. 
But  here  is  one  instance,  out  of  many,  of  the  polyglot  character 
of  the  Jesuit  body,  and  its  advantages  in  literature. 

Philippi  Lausbergii  Cyclometrise  Novsa  Libri  Duo.    Middleburg, 
1616,  4to. 

This  is  one  of  the  legitimate  quadratures,  on  which  I  shall 
here  only  remark  that  by  candlelight  it  is  quadrature  under 
difficulties,  for  all  the  diagrams  are  in  red  ink. 

Recherches  Curieuses  des  Mesures  du   Monde.     By  S.  C.  de  V. 
Paris,  1626,  8vo.  (pp.  48). 

It  is  written  by  some  Count  for  his  son  ;  and  if  all  the  French 
nobility  would  have  given  their  sons  the  same  kind  of  instruction 
about  rank,  the  old  French  aristocracy  would  have  been  as  pros- 
perous at  this  moment  as  the  English  peerage  and  squireage.  I 
sent  the  tract  to  Capt.  Speke,  shortly  after  his  arrival  in  England, 
thinking  he  might  like  to  see  the  old  names  of  the  Ethiopian  pro- 
vinces. But  I  first  made  a  copy  of  all  that  relates  to  Prester  John, 
himself  a  paradox.  The  tract  contains,  inter  alia,  an  account  of 


PRESTER  JOHN.  47 

the  four  empires ;  of  the  great  Turk,  the  great  Tartar,  the  great 
Sophy,  and  the  great  Prester  John.  This  word  great  (grand), 
which  was  long  used  in  the  phrase  '  the  great  Turk,'  is  a  generic 
adjunct  to  an  emperor.  Of  the  Tartars  it  is  said  that  '  c'est  vne 
nation  prophane  et  barbaresque,  sale  et  vilaine,  qui  mangent  la 
chair  demie  crue,  qui  boiuent  du  laict  de  jument,  et  qui  n'vsent 
de  nappes  et  seruiettes  que  pour  essuyer  leurs  bouches  et  leurs 
mains.'  Many  persons  have  heard  of  Prester  John,  and  have 
a  very  indistinct  idea  of  him.  I  give  all  that  is  said  about  him, 
since  the  recent  discussions  about  the  Nile  may  give  an  interest 
to  the  old  notions  of  geography. — 

Le  grand  Prestre  Jean  qui  est  le  quatriesme  en  rang,  est  Empereur 
d'Ethiopie,  et  des  Abyssins,  et  se  vante  d'estre  issu  de  la  race  de  Dauid, 
comme  estant  descendu  de  la  Boyne  de  Saba,  Boyne  d'Ethiopie,  laqu?lle 
estant  venue  en  Hierusalem  pour  voir  la  sagesse  de  Salomou,  enuiron 
1'an   du   monde  2952,  s'en  retourna  grosse  d'vn  fils  qu'ils  nomment 
Moylech,  duquel  ils  disent  estre  descendus  en  ligne  directe.     Et  ainsi 
il  se  glorifie  d'estre  le  plus  ancien  Monarque  de  la  terre,  disant  que  son 
Empire  a  dure  plus  de  trois  mil  ans,  ce  que  nul  autre  Empire  ne  pent 
dire.     Aussi  met-il  en  ses  tiltres  ce  qui  s'ensuit :  Nous,  N.  Souuerain 
en  mes  Royaumes,  vniquement  ayme  de  Dieu,  colomne  de  la  foy,  sorty 
de  la  race  de  luda,  &c.     Les  limites  de  cet  Empire  touchent  a  la  mer 
Ronge,    et   aux   montagnes    d'Azuma   vers   1'Orient,    et   du  coste  de 
1' Occident,  il  est  borne  du  fleuue  du  Nil,  qui  le  separe  de  la  Nubie,  vers 
le  Septentrion  il  a  1'^Egypte,  et  au  Midy  les  Royaumes  de  Congo,  et  de 
Mozambique,   sa  longueur  contenant  quarante  degre,   qui  font   mille 
vingt  cinq  lieues,  et  ce  depuis  Congo  on  Mozambique  qui  sont  au  Midy, 
iusqu'en  ^-Egypte  qui  est  au  Septentrion,  et  sa  largeur  contenant  depuis 
le  Nil  qui  est  a  1' Occident,  iusqu'aux  montagnes  d'Azuma,  qui  sont  a 
1'Orient,  sept  cens  vingt  cinq  lieues,  qui  font  vingt  neuf  degrez.     Get 
empire  a  sous  soy  trente  grandes  Prouinces,   scavoir,  Medra,  Gaga, 
Alchy,    Cedalon,    Mantro,    Finazam,    Barnaquez,     Ambiam,     Fungy, 
Angote,  Cigremaon,   Gorga  Cafatez,  Zastanla,  Zeth,  Barly,  Belangana, 
Tygra,    Gorgany,   Barganaza,   d'Ancut,   Dargaly  Ambiacatina,   Cara- 
cogly,    Amara    .     Maon  (sic),  Guegiera,  Bally,  Dobora   et  Macheda. 
Toutes  ces  Prouinces  cy  dessus  sont  situees  iustement  sous  la  ligne 
equinoxiale,  entres  les  Tropiques  de  Capricorne,  et  de  Cancer.     Mais 
elles  s'approchent  de  nostre   Tropiqne,  de  deux  cens  cinquante  lieues 
plus  qu' elles  ne  font  de  I'autre  Tropique.     Ce  mot  de  Prestre  Jean 
signifie  grand  Seigneur,  et  n'est  pas  Prestre  comme  plusieurs  pense,  il  a 
este  tousiours  Chrestien,  mais  souuent  Schismatique  :  maintenant  il  est 
Catholique,  et  reconnaist  le  Pape  pour  Sounerain  Pontife.     I'ay  veu 
quelqu'vn  des  ses  Euesques,  estant  en  Hierusalem,  auec  lequel  i'ay 
confere  souuent  par  le  moyen  de  nostre  trucheman :  il  estoit  d'vn  port 
graue  et  serieux,  succiur  (sic)  en  son  parler,  mais  subtil  a  merueilles 
en  tout  ce  qu'il  disoit.     II  prenoit   grand  plaisir  au  recit  (me  je  luy 


48  A  BUDGET   OF  PARADOXES. 

faisais  de  nos  belles  ceremonies,  et  de  la  granite  de  nos  Prelats  enleurs 
habits  Pontificaux,  et  autres  choses  que  je  laisse  pour  dire,  que  1'Ethi- 
opien  est  ioyoux  et  gaillard,  ne  ressemblant  en  rien  a  la  salete  du  Tar- 
tare,  ny  a  1'affreux  regard  du  miserable  Arabe,  mais  ils  sont  fins  et 
cauteleux,  et  ne  se  fient  en  personne,  soup9onneux  a  merueilles,  et  fort 
devotieux,  ils  ne  sont  du  tout  noirs  comme  1'on  croit,  i'entens  parler  de 
ceux  qui  ne  sont  pas  sous  la  ligne  Equinoxiale,  ny  trop  proches  d'icelle, 
car  ceux  qui  sont  dessous  sont  les  Mores  que  nous  voyons. 

It  will  be  observed  that  the  author  speaks  of  his  conversation 
with  an  Ethiopian  bishop,  about  that  bishop's  sovereign.  Some- 
thing must  have  passed  between  the  two  which  satisfied  the 
writer  that  the  bishop  acknowledged  his  own  sovereign  under 
some  title  answering  to  Prester  John. 

De  Cometa  anni  1618  dissertationes  Thomae  Fieni  et  Liberti 
Fromondi.  .  .  Equidem  Thomee  Fieni  epistolica  queBstio,  An 
verum  sit  Coelum  moveri  et  Terram  quiescere  ?  London,  1670, 
8vo. 

This  tract  of  Fienus  against  the  motion  of  the  earth  is  a  reprint 
of  one  published  in  1619.  I  have  given  an  account  of  it  as  a 
good  summary  of  arguments  of  the  time,  in  the  Companion  to  the 
Almanac  for  1836. 

Willebrordi  Snellii.     R.  F.  Cyclometricus.     Leyden,  1621,  4to. 

This  is  a  celebrated  work  on  the  approximative  quadrature, 
which,  having  the  suspicious  word  oyclometricus,  must  be  noticed 
here  for  distinction. 

1620.  In  this  year,  Francis  Bacon  published  his  'Novum 
Organum,'  which  was  long  held  in  England — but  not  until  the 
last  century — to  be  the  work  which  taught  Newton  and  all  his 
successors  how  to  philosophise.  That  Newton  never  mentions 
Bacon,  nor  alludes  in  any  way  to  his  works,  passed  for  nothing. 
Here  and  there  a  parodoxer  ventured  not  to  find  all  this  teaching 
in  Bacon,  but  he  was  pronounced  blind.  In  our  day  it  begins 
to  be  seen  that,  great  as  Bacon  was,  and  great  as  his  book  really 
is,  he  is  not  the  philosophical  father  of  modern  discovery. 

But  old  prepossession  will  find  reason  for  anything.  A  learned 
friend  of  mine  wrote  to  me  that  he  had  discovered  proof  that 
Newton  owned  Bacon  for  his  master :  the  proof  was  that  Newton, 
in  some  of  his  earlier  writings,  used  the  phrase  experimentum 
crucis,  which  is  Bacon's.  Newton  may  have  read  some  of  Bacon, 
though  no  proof  of  it  appears.  I  have  a  dim  idea  that  I  once 
saw  the  two  words  attributed  to  the  alchemists :  if  so,  there  is 


FRANCIS   BACON.  49 

another  explanation ;  for  Newton   was   deeply  read   in   the   al- 
chemists. 

I  subjoin  a  review  which  I  wrote  of  the  splendid  edition  of 
Bacon  by  Spedding,  Ellis,  and  Heath.  All  the  opinions  therein 
expressed  had  been  formed  by  me  long  before :  most  of  the 
materials  were  collected  for  another  purpose. 

The   Works   of  Francis    Bacon.      Edited   by    James    Spedding, 
R.  Leslie  Ellis,  and  Douglas  D.  Heath.     5  vols. 

No  knowledge  of  nature  without  experiment  and  observation  : 
so  said  Aristotle,  so  said  Bacon,  so  acted  Copernicus,  Tycho  Brahe, 
Gilbert,  Kepler,  Galileo,  Harvey,  &c.,  before  Bacon  wrote.  No 
derived  knowledge  until  experiment  and  observation  are  con- 
cluded :  so  said  Bacon,  and  no  one  else.  We  do  not  mean  to  say 
that  he  laid  down  his  principle  in  these  words,  or  that  he  carried 
it  to  the  utmost  extreme :  we  mean  that  Bacon's  ruling  idea  was 
the  collection  of  enormous  masses  of  facts,  and  then  digested 
processes  of  arrangement  and  elimination,  so  artistically  contrived, 
that  a  man  of  common  intelligence,  without  any  unusual  sagacity, 
should  be  able  to  announce  the  truth  sought  for.  Let  Bacon 
speak  for  himself,  in  his  editor's  English  : — 

But  the  course  I  propose  for  the  discovery  of  sciences  is  such  as 
leaves  but  little  to  the  acuteness  and  strength  of  wits,  but  places  all  wits 
and  understandings  nearly  on  a  level.  For,  as  in  the  drawing  of  a  straight 
line  or  a  perfect  circle,  much  depends  on  the  steadiness  and  practice  of 
the  hand,  if  it  be  done  by  aim  of  hand  only,  but  if  with  the  aid  of  rule 
or  compass  little  or  nothing,  so  it  is  exactly  with  my  plan.  .  .  For 
my  way  of  discovering  sciences  goes  far  to  level  men's  wits,  and  leaves 
but  little  to  individual  excellence ;  because  it  performs  everything  by 
the  surest  rules  and  demonstrations. 

To  show  that  we  do  not  strain  Bacon's  meaning,  we  add  what 
is  said  by  Hooke,  whom  we  have  already  mentioned  as  his  pro- 
fessed disciple,  and,  we  believe,  his  only  disciple  of  the  day  of 
Newton.  We  must,  however,  remind  the  reader  that  Hooke  was 
very  little  of  a  mathematician,  and  spoke  of  algebra  from  his  own 
idea  of  what  others  had  tol'd  him  : — 

The  intellect  is  not  to  be  suffered  to  act  without  its  helps,  but  is 
continually  to  be  assisted  by  some  method  or  engine,  which  shall 
be  as  a  guide  to  regulate  its  actions,  so  as  that  it  shall  not  be  able  to 
act  amiss.  Of  this  engine,  no  man  except  the  incomparable  Verulam 
hath  had  any  thoughts,  and  he  indeed  hath  promoted  it  to  a  very  good 
pitch  ;  but  there  is  yet  somewhat  more  to  be  added,  which  lie  seemed 
to  want  time  to  complete.  By  this,  as  by  that  art  of  algebra  in  geo- 

£ 


50  A  BUDGET   OF  PARADOXES. 

metry,  'twill  be  very  easy  to  proceed  in  any  natural  inquiry,  regularly 
and  certainly.  .  .  For  as  'tis  very  hard  for  the  most  acute  wit  to  find 
out  any  difficult  problem  in  geometry  without  the  help  of  algebra  .  .  . 
and  altogether  as  easy  for  the  meanest  capacity  acting  by  that  method 
to  complete  and  perfect  it,  so  will  it  be  in  the  inquiry  after  natural 
.  knowledge. 

Bacon  did  not  live  to  mature  the  whole  of  this  plan.  Are  we 
really  to  believe  that  if  he  had  completed  the  '  Instauratio '  we 
who  write  this — and  who  feel  ourselves  growing  bigger  as  we 
write  it — should  have  been  on  a  level  with  Newton  in  physical 
discovery?  Bacon  asks  this  belief  of  us,  and  does  not  get  it. 
But  it  may  be  said,  Your  business  is  with  what  he  did  leave, 
and  with  its  consequences.  Be  it  so.  Mr.  Ellis  says  :  l  That  his 
method  is  impracticable  cannot,  I  think,  be  denied,  if  we  reflect 
not  only  that  it  never  has  produced  any  result,  but  also  that  the 
process  by  which  scientific  truths  have  been  established  cannot 
be  so  presented  as  even  to  appear  to  be  in  accordance  with  it.' 
That  this  is  very  true  is  well  known  to  all  who  have  studied  the 
history  of  discovery :  those  who  deny  it  are  bound  to  establish 
either  that  some  great  discovery  has  been  made  by  Bacon's 
method — we  mean  by  the  part  peculiar -to  Bacon — or,  better  still, 
to  show  that  some  new  discovery  can  be  made,  by  actually  making- 
it.  No  general  talk  about  induction :  no  reliance  upon  the 
mere  fact  that  certain  experiments  or  observations  have  been 
made  ;  let  us  see  where  Bacon's  induction  has  been  actually 
used  or  can  be  used.  Mere  induction,  enumeratio  simplex,  is 
spoken  of  by  himself  with  contempt,  as  utterly  incompetent. 
For  Bacon  knew  well  that  a  thousand  instances  may  be  contra- 
dicted by  the  thousand  and  first :  so  that  no  enumeration  of 
instances,  however  large,  is  '  sure  demonstration,'  so  long  as  any 
are  left. 

The  immortal  Harvey,  who  was  inventing — we  use  the  word 
in  its  old  sense — the  circulation  of  the  blood,  while  Bacon  was  in 
,  the  full  flow  of  thought  upon  his  system,  may  be  trusted  to  say 
whether,  when  the  system  appeared,  he  found  any  likeness  in  it 
to  his  own  processes,  or  what  would  have  been  any  help  to  him, 
if  he  had  waited  for  the  '  Novum  Organum.'  He  said  of  Bacon, 
*  He  writes  philosophy  like  a  Lord  Chancellor.'  This  has  been 
generally  supposed  to  be  only  a  sneer  at  the  sutor  ultra  crepidam ; 
but  we  cannot  help  suspecting  that  there  was  more  intended  by 
it.  To  us,  Bacon  is  eminently  the  philosopher  of  error  prevented, 
not  of  progress  facilitated.  When  we  throw  off  the  idea  of  being 
led  right,  and  betake  ourselves  to  that  of  being  kept  from  going 


FRANCIS   BACON.  51 

wrong,  we  read  his  writings  with  a  sense  of  their  usefulness,  his 
genius,  and  their  probable  effect  upon  purely  experimental  science, 
which  we  can  be  conscious  of  upon  no  other  supposition.  It 
amuses  us  to  have  to  add  that  the  part  of  Aristotle's  logic  of 
which  he  saw  the  value  was  the  book  on  refutation  of  fallacies. 
Now  is  this  not  the  notion  of  things  to  which  the  bias  of  a 
practised  lawyer  might  lead  him  ?  In  the  case  which  is  before 
the  Court,  generally  speaking,  truth  lurks  somewhere  about  the 
facts,  and  the  elimination  of  all  error  will  show  it  in  the  residuum. 
The  two  senses  of  the  word  law  come  in  so  as  to  look  almost  like 
a  play  upon  words.  The  judge  can  apply  the  law  so  soon  as  the 
facts  are  settled  :  the  physical  philosopher  has  to  deduce  the  law 
from  the  facts.  Wait,  says  the  judge,  until  the  facts  are  deter- 
mined :  did  the  prisoner  take  the  goods  with  felonious  intent  ? 
did  the  defendant  give  what  amounts  to  a  warranty  ?  or  the  like. 
Wait,  says  Bacon,  until  all  the  facts,  or  all  the  obtainable  facts, 
are  brought  in  :  apply  my  rules  of  separation  to  the  facts,  and  the 
result  shall  come  out  as  easily  as  by  ruler  and  compasses.  We  think 
it  possible  that  Harvey  might  allude  to  the  legal  character  of 
Bacon's  notions :  we  can  hardly  conceive  so  acute  a  man,  after 
seeing  what  manner  of  writer  Bacon  was,  meaning  only  that  he 
was  a  lawyer  and  had  better  stick  to  his  business.  We  do  our- 
selves believe  that  Bacon's  philosophy  more  resembles  the  action 
of  mind  of  a  common-law  judge — not  a  Chancellor — than  that  of 
the  physical  inquirers  who  have  been  supposed  to  follow  in  his 
steps.  It  seems  to  us  that  Bacon's  argument  is,  there  can  be 
nothing  of  law  but  what  must  be  either  perceptible,  or  mechani- 
cally deducible,  when  all  the  results  of  law,  as  exhibited  in 
phenomena,  are  before  us.  Now  the  truth  is,  that  the  physical 
philosopher  has  frequently  to  conceive  law  which  never  was  in  his 
previous  thought — to  educe  the  unknown,  not  to  choose  among 
the  known.  Physical  discovery  would  be  very  easy  work  if  the 
inquirer  could  lay  down  his  this,  his  that,  and  his  t'other,  and  say, 
'  Now,  one  of  these  it  must  be ;  let  us  proceed  to  try  which.' 
Often  has  he  done  this,  and  failed ;  often  has  the  truth  turned 
out  to  be  neither  this,  that,  nor  t'other.  Bacon  seems  to  us  to 
think  that  the  philosopher  is  a  judge  who  has  to  choose,  upon 
ascertained  facts,  which  of  known  statutes  is  to  rule  the  decision : 
he  appears  to  us  more  like  a  person  who  is  to  write  the  statute- 
book,  with  no  guide  except  cases  and  decisions  presented  in  all 
their  confusion  and  all  their  conflict. 

Let    us    take   the    well-known  first  aphorism  of  the  '  Novum 
Organum  : ' 

B   2 


52  A  BUDGET  OF  PAEA  BOXES. 

Man  being  the  servant  and  interpreter  of  nature,  can  do  and  under- 
stand so  much,  and  so  much  only,  as  he  has  observed  in  fact  or  in 
thought  of  the  course  of  nature  :  beyond  this  he  neither  knows  anything 
nor  can  do  anything. 

This  aphorism  is  placed  by  Sir  John  Herschel  at  the  head  of 
his  '  Discourse  on  the  Study  of  Natural  Philosophy  : '  a  book  con- 
taining notions  of  discovery  far  beyond  any  of  which  Bacon  ever 
dreamed ;  and  this  because  it  was  written  after  discovery,  instead 
of  before.  Sir  John  Herschel,  in  his  version,  has  avoided  the 
translation  of  re  vel  mente  observaverit,  and  gives  us  only  '  by  his 
observation  of  the  order  of  nature.'  In  making  this  the  opening 
of  an  excellent  sermon,  he  has  imitated  the  theologians,  who 
often  employ  the  whole  time  of  the  discourse  in  stuffing  matter 
into  the  text,  instead  of  drawing  matter  out  of  it.  By  observation 
he  (Herschel)  means  the  whole  course  of  discovery,  observation, 
hypothesis,  deduction,  comparison,  &c.  The  type  of  the  Baconian 
philosopher,  as  it  stood  in  his  mind,  had  been  derived  from  a 
noble  example,  his  own  father,  William  Herschel,  an  inquirer 
whose  processes  would  have  been  held  by  Bacon  to  have  been 
vague,  insufficient,  compounded  of  chance  work  and  sagacity,  and 
too  meagre  of  facts  to  deserve  the  name  of  induction.  In  another 
work,  his  treatise  on  Astronomy,  Sir  John  Herschel,  after  noting 
that  a  popular  account  can  only  place  the  reader  on  the  threshold, 
proceeds  to  speak  as  follows  of  all  the  higher  departments  of 
science.  The  italics  are  his  own  : — 

Admission  to  its  sanctuary,  and  to  the  privileges  and  feelings  of 
a  votary,  is  only  to  be  gained  by  one  means — sound  and  sufficient 
knowledge  of  mathematics,  tJte  great  instrument  of  all  exact  inquiry, 
without  which  no  man  can  ever  make  such  advances  in  this  or  any  other 
of  the  higher  departments  of  science  as  can  entitle  him.  to  form  an  inde- 
pendent opinion  on  any  subject  of  discussion  within  their  range. 

How  is  this?  Man  can  know  no  more  than  he  gets  from 
observation,  and  yet  mathematics  is  the  great  instrument  of  all 
exact  inquiry.  Are  the  results  of  mathematical  deduction  results 
of  observation  ?  We  think  it  likely  that  Sir  John  Herschel 
would  reply  that  Bacon,  in  coupling  together  observare  re  and 
observare  mente,  has  done  what  some  wags  said  Newton  afterwards 
did  in  his  study-door — cut  a  large  hole  of  exit  for  the  large  cat, 
and  a  little  hole  for  the  little  cat.  But  Bacon  did  no  such  thing : 
he  never  included  any  deduction  under  observation.  To  mathe- 
matics he  had  a  dislike.  He  averred  that  logic  and  mathematics 
should  be  the  handmaids,  not  the  mistresses,  of  philosophy.  He 
ineant  that  they  should  play  a  subordinate  and  subsequent  part 


FRANCIS   BACON.  53 

in  the  dressing  of  the  vast  mass  of  facts  by  which  discovery  was 
to  be  rendered  equally  accessible  to  Newton  and  to  us.  Bacon 
himself  was  very  ignorant  of  all  that  had  been  done  by  mathe- 
matics ;  and,  strange  to  say,  he  especially  objected  to  astronomy 
being  handed  over  to  the  mathematicians.  Leverrier  and  Adams, 
calculating  an  unknown  planet  into  visible  existence  by  .enormous 
heaps  of  algebra,  furnish  the  last  comment  of  note  on  this 
specimen  of  the  goodness  of  Bacon's  views.  The  following 
account  of  his  knowledge  of  what  had  been  done  in  his  own  day 
or  before  it,  is  Mr.  Spedding's  collection  of  casual  remarks  in 
Mr.  Ellis's  several  prefaces  : — 

Though  he  paid  great  attention  to  astronomy,  discussed  carefully  the 
methods  in  which  it  ought  to  be  studied,  constructed  for  the  sati? fac- 
tion of  his  own  mind  an  elaborate  theory  of  the  heavens,  and  listened 
eagerly  for  the  news  from  the  stars  brought  by  Galileo's  telescope,  he 
appears  to  have  been  utterly  ignorant  of  the  discoveries  which  had 
just  been  made  by  Kepler's  calculations.     Though,  he  complained  in 
1623  of  the  want  of  compendious  methods  for  facilitating  arithmetical 
computations,  especially  with  regard  to  the  doctrine  of  Series,  and 
fully  recognized  the  importance  of  them  as  an  aid  to  physical  inquiries — 
he   does  not  say  a  word  about  Napier's  Logarithms,  which  had  been 
published  only  nine  years  before  and  reprinted  more  than  once  in  the 
interval.     He  complained  that  no  considerable  advance  had  been  made 
in  geometry  beyond  Euclid,  without  taking  any  notice  of  what  Lad 
been    done  by  Archimedes  and  Apollonius.     He  saw  the  importance  of 
determining  accurately  the  specific  gravities  of  different  substances,  and 
himself  attempted  to  form  a  table  of  them  by  a  rude  process  of  his  own, 
without  knowing  of  the  more  scientific  though  still  imperfect  methods 
previously  employed  by  Archimedes,  Ghetaldus,  and  Porta.     He  speaks 
of  the  tvpijxa  of  Archimedes  in  a  manner  which  implies  that  he  did  not 
clearly  apprehend  either  the  nature  of  the  problem  to  be  solved  or  the 
principles  upon  which  the  solution  depended.     In  reviewing  the  pro- 
gress of  mechanics,  he  makes  no  mention  of  Archimedes  himself,  or  of 
Stevinus,  Galileo.  Guldinus,  or  Ghetaldus.     He  makes  no  allusion  to 
the  theory  of  equilibrium.   He  observes  that  a  ball  of  one  pound  weight 
will  fall  nearly  as  fast  through  the  air  as  a  ball  of  two,  without  alluding 
to  the  theory  of  the  acceleration  of  falling  bodies,  which  had  been 
made  known  by  Galileo  more  than  thirty  years  before.     He  proposes  an 
inquiry  with  regard  to  the  lever — namely,  whether  in  a  balance  with 
arms  of  different  length  but  equal  weight  the  distance  from  the  fulcrum 
has  any  effect  upon  the  inclination, — though  the  theory  of  the  lever  was 
as  well  understood  in  his  own  time  as  it  is  now.     In  making  an  experi- 
ment of  his  own  to  ascertain  the  cause  of  the  motion  of  a  windmill,  he 
overlooks  an  obvious  circumstance  which  makes  the  experiment  incon- 
clusive, and  an  equally  obvious  variation  of  the  same  experiment  which 
would  Lave  sLown  Lim  that  Lis  tLeory  was  false.     He  speaks  of  the 


54  A  BUDGET   OF  PARADOXES. 

poles  of  the  earth  as  fixed,  in  a  manner  which  seems  to  imply  that  he 
was  not  acquainted  with  the  precession  of  the  equinoxes  ;  and  in 
another  place,  of  the  north  pole  being  above  and  the  south  pole  below, 
as  a  reason  why  in  our  hemisphere  the  north  winds  predominate  over 
the  south. 

Much  of  this  was  known  before,  but  such  a  summary  of  Bacon's 
want  of  knowledge  of  the  science  of  his  own  time  was  never  yet 
collected  in  one  place.  We  may  add,  that  Bacon  seems  to  have 
been  as  ignorant  of  Wright's  memorable  addition  to  the  resources 
of  navigation  as  of  Napier's  addition  to  the  means  of  calculation. 
Mathematics  was  beginning  to  be  the  great  instrument  of  exact 
inquiry :  Bacon  threw  the  science  aside,  from  ignorance,  just  at 
the  time  when  his  enormous  sagacity,  applied  to  knowledge, 
would  have  made  him  see  the  part  it  was  to  play.  If  Newton 
had  taken  Bacon  for  his  master,  not  he,  but  somebody  else,  would 
have  been  Newton. 

There  is  an  attempt  at  induction  going  on,  which  has  yielded 
little  or  no  fruit,  the  observations  made  in  the  meteorological 
observatories.  This  attempt  is  carried  on  in  a  manner  which 
would  have  caused  Bacon  to  dance  for  joy  ;  for  he  lived  in  times 
when  Chancellors  did  dance.  Eussia,  says  M.  Biot,  is  covered  by 
an  army  of  meteorographs,  with  generals,  high  officers,  subalterns, 
and  privates  with  fixed  and  defined  duties  of  observation.  Other 
countries  have  also  their  systematic  observations.  And  what  has 
come  of  it  ?  Nothing,  says  M.  Biot,  and  nothing  will  ever  come 
of  it :  the  veteran  mathematician  and  experimental  philosopher 
declares,  as  does  Mr.  Ellis,  that  no  single  branch  of  science  has 
ever  been  fruitfully  explored  in  this  way.  There  is  no  special 
object,  he  says.  Any  one  would  suppose  that  M.  Biot's  opinion, 
given  to  the  French  Government  upon  the  proposal  to  construct 
meteorological  observatories  in  Algeria  (Comptes  Rendue,vol.  xli, 
Dec.  31,  1855),  was  written  to  support  the  mythical  Bacon,  modern 
physics,  against  the  real  Bacon  of  the  '  Novum  Organum.'  There 
is  no  special  object.  In  these  words  lies  the  difference  between 
the  two  methods. 

[In  the  report  to  the  Greenwich  Board  of  Visitors  for  1867, 
Mr.  Airy,  speaking  of  the  increase  of  meteorological  observatories, 
remarks  '  Whether  the  effect  of  this  movement  will  be  that 
millions  of  useless  observations  will  be  added  to  the  millions  that 
already  exist,  or  whether  something  may  be  expected  to  result 
which  will  lead  to  a  meteorological  theory,  I  cannot  hazard  a 
conjecture.'  This  is  a  conjecture,  and  a  very  obvious  one :  if 


i'RANCIS   BACON.  55 

Mr.  Airy  would  have  given  2f  cZ.  for  the  chance  of  a  meteorological 
theory  formed  by  masses  of  observations,  he  would  never  have 
said  what  I  have  quoted.] 

Modern  discoveries  have  not  been  made  by  large  collections  of 
facts,  with  subsequent  discussion,  separation,  and  resulting  de- 
duction of  a  truth  thus  rendered  perceptible.  A  few  facts  have 
suggested  an  hypothesis,  which  means  a  supposition,  proper  to 
explain  them.  The  necessary  results  of  this  supposition  are 
worked  out,  and  then,  and  not  till  then,  other  facts  are  examined 
to  see  if  these  ulterior  results  are  found  in  nature.  The  trial  of 
the  hypothesis  is  the  special  object:  prior  to  which,  hypothesis 
must  have  been  started,  not  by  rule,  but  by  that  sagacity  of 
which  no  description  can  be  given,  precisely  because  the  very 
owners  of  it  do  not  act  under  laws  perceptible  to  themselves. 
The  inventor  of  hypothesis,  if  pressed  to  explain  his  method,  must 
answer  as  did  Zerah  Colburn,  when  asked  for  his  mode  of  instan- 
taneous calculation.  When  the  poor  boy  had  been  bothered  for 
some  time  in  this  manner,  he  cried  out  in  a  huff,  '  God  put  it 
into  my  head,  and  I  can't  put  it  into  yours.'  Wrong  hypotheses, 
rightly  worked  from,  have  produced  more  useful  results  than 
unguided  observation.  But  this  is  not  the  Baconian  plan. 
Charles  the  Second,  when  informed  of  the  state  of  navigation, 
founded  a  Baconian  observatory  at  Greenwich,  to  observe,  observe, 
observe  away  at  the  moon,  until  her  motions  were  known  suf- 
ficiently well  to  render  her  useful  in  guiding  the  seaman.  And 
no  doubt  Flamsteed's  observations,  twenty  or  thirty  of  them 
at  least,  were  of  signal  use.  But  how?  A  somewhat  fanciful 
thinker,  one  Kepler,  had  hit  upon  the  approximate  orbits  of  the 
planets  by  trying  one  hypothesis  after  another :  he  found  the 
ellipse,  which  the  Platonists,  well  despised  of  Bacon,  and  who 
would  have  despised  him  as  heartily  if  they  had  known  him,  had 
investigated  and  put  ready  to  hand  nearly  2,000  years  before. 
The  sun  in  the  focus,  the  motions  of  the  planet  more  and  more 
rapid  as  they  approach  the  sun,  led  Kepler — and  Bacon  would 
have  reproved  him  for  his  rashness — to  imagine  that  a  force  re- 
siding in  the  sun  might  move  the  planets,  a  force  inversely  as  the 
distance.  Bouillaud,  upon  a  fanciful  analogy,  rejected  the  inverse 
distance,  and,  rejecting  the  force  altogether,  declared  that  if  such 
a  thing  there  were,  it  would  be  as  the  inverse  square  of  the 
distance.  Newton,  ready  prepared  with  the  mathematics  of  the 
subject,  tried  the  fall  of  the  moon  towards  the  earth,  away  from 
her  tangent,  and  found  that,  as  compared  with  the  fall  of  a  stone, 


56  A  BUDGET   OF  PARADOXES. 

the  law  of  the  inverse  square  did  hold  for  the  moon.  He  deduced 
the  ellipse,  he  proceeded  to  deduce  the  effect  of  the  disturbance 
of  the  sun  upon  the  moon,  upon  the  assumed  theory  of  universal 
gravitation.  He  found  result  after  result  of  his  theory  in  con- 
formity with  observed  fact :  and,  by  aid  of  Flamsteed's  obser- 
vations, which  amended  what  mathematicians  call  his  constants, 
he  constructed  his  lunar  theory.  Had  it  not  been  for  Newton, 
the  whole  dynasty  of  Greenwich  astronomers,  from  Flamsteed  of 
happy  memory,  to  Airy  whom  Heaven  preserve,  might  have 
worked  away  at  nightly  observation  and  daily  reduction,  without 
any  remarkable  result :  looking  forward,  as  to  a  millennium,  to 
the  time  when  any  man  of  moderate  intelligence  was  to  see 
the  whole  explanation.  What  are  large  collections  of  facts  for  ? 
To  make  theories  from.,  says  Bacon :  to  try  ready-made  theories 
by,  says  the  history  of  discovery  :  it's  all  the  same,  says  the 
idolater  :  nonsense,  say  we  ! 

Time  and  space  run  short :  how  odd  it  is  that  of  the  three 
leading  ideas  of  mechanics,  time,  space,  and  matter,  the  first  two 
should  always  fail  a  reviewer  before  the  third.  We  might  dwell 
upon  many  points,  especially  if  we  attempted  a  more  descriptive 
account  of  the  valuable  edition  before  us.  No  one  need  imagine 
that  the  editors,  by  their  uncompromising  attack  upon  the  notion 
of  Bacon's  influence  common  even  among  mathematicians  and 
experimental  philosophers,  have  lowered  the  glory  of  the  great 
man  whom  it  was,  many  will  think,  their  business  to  defend 
through  thick  and  thin.  They  have  given  a  clearer  notion  of  his 
excellencies,  and  a  better  idea  of  the  power  of  his  mind,  than  ever 
we  saw  given  before.  Such  a  correction  as  theirs  must  have  come, 
and  soon,  for  as  Hallam  says — after  noting  that  the  'Novum 
Organum'  was  never  published  separately  in  England,  Bacon  has 
probably  been  more  read  in  the  last  thirty  years — now  forty — than 
in  the  two  hundred  years  which  preceded.  He  will  now  be  more 
read  than  ever  he  was.  The  history  of  the  intellectual  world  is 
the  history  of  the  worship  of  one  idol  after  another.  No  sooner 
is  it  clear  that  a  Hercules  has  appeared  among  men,  than  all 
that  imagination  can  conceive  of  strength  is  attributed  to  him, 
and  his  labours  are  recorded  in  the  heavens.  The  time  arrives 
when,  as  in  the  case  of  Aristotle,  a  new  deity  is  found,  and  the 
old  one  is  consigned  to  shame  and  reproach.  A  reaction  may 
afterwards  take  place,  and  this  is  now  happening  in  the  case  of 
the  Greek  philosopher.  The  end  of  the  process  is,  that  the  oppo- 
sing deities  take  their  places,  side  by  side,  in  a  Pantheon  dedicated 
pot  to  gods,  but  to  heroes. 


COPERNICUS  AND   THE  POPE.  57 

Passing  over  the  success  of  Bacon's  own  endeavours  to  improve 
the  details  of  physical  science,  which  was  next  to  nothing,  and  of 
his  method  as  a  whole,  which  has  never  been  practised,  we  might 
say  much  of  the  good  influence  of  his  writings.  Sound  wisdom, 
set  in  sparkling  wit,  must  instruct  and  amuse  to  the  end  of  time  : 
and,  as  against  error,  we  repeat  that  Bacon  is  soundly  wise,  so  far 
as  he  goes.  There  is  hardly  a  form  of  human  error  within  his 
scope  which  he  did  not  detect,  expose,  and  attach  to  a  satirical 
metaphor  which  never  ceases  to  sting.  He  is  largely  indebted  to 
a  very  extensive  reading  ;  but  the  thoughts  of  others  fall  into  his 
text  with  such  a  close-fitting  compactness  that  he  can  make  even 
the  words  of  the  Sacred  Writers  pass  for  his  own.  A  saying  of 
the  prophet  Daniel,  rather  a  hackneyed  quotation  in  our  day, 
Multi  pertransibunt,  et  augebitur  scientia,  stands  in  the  title-page 
of  the  first  edition  of  Montucla's  '  History  of  Mathematics '  as  a 
quotation  from  Bacon — and  it  is  not  the  only  place  in  which  this 
mistake  occurs.  When  the  truth  of  the  matter,  as  to  Bacon's 
system,  is  fully  recognized,  we  have  little  fear  that  there  will  be 
a  reaction  against  the  man.  First,  because  Bacon  will  always 
live  to  speak  for  himself,  for  he  will  not  cease  to  be  read  : 
secondly,  because  those  who  seek  the  truth  will  find  it  in  the 
best  edition  of  his  works,  and  will  be  most  ably  led  to  know  what 
Bacon  was,  in  the  very  books  which  first  showed  at  large  what  he 
was  not. 

In  this  year  (1620)  appeared  the  corrections  under  which  the 
Congregation  of  the  Index  —  i.e.  the  Committee  of  Cardinals 
which  superintended  the  Index  of  forbidden  books — proposed  to 
allow  the  work  of  Copernicus  to  be  read.  I  insert  these  con- 
ditions in  full,  because  they  are  often  alluded  to,  and  I  know  of 
no  source  of  reference  accessible  to  a  twentieth  part  of  those  who 
take  interest  in  the  question. 

By  a  decree  of  the  Congregation  of  the  Index,  dated  March  5, 
1616,  the  work  of  Copernicus,  and  another  of  Didacus  Astunica, 
are  suspended  donee  coirigantur,  as  teaching  : 

'  Falsam  iilam  doctrinam  Pythagoricam,divinae  que  Scripturje  omnino 
adversantem,  de  mobilitate  Terras  et  immobilitate  Solis.' 

But  a  work  of  the  Carmelite  Foscarini  is  : 

'  Omnino  prohibendura  atque  damnandum,' because  'ostendere  conatur 
prasfatani  doctrinam  ....  consonam  esse  veritati  et  non  adversari 
Sacra3  Sci-iptura3.' 

Works  which   teach  the  false  doctrine  of  the  earth's  motion 


58  A  BUDGET  OF  PARADOXES. 

are  to  be  corrected  ;  those  which  declare  the  doctrine  conformable 
to  Scripture  are  to  be  utterly  prohibited. 

In  a  ;  Monitum  ad  Nicolai  Copernici  lectorem,  ej  usque  emen- 
datio,  permissio,  et  correctio,'  dated  1620  without  the  month  or 
day,  permission  is  given  to  reprint  the  work  of  Copernicus  with 
certain  alterations  ;  and,  by  implication,  to  read  existing  copies 
after  correction  in  writing.  In  the  preamble  the  author  is  called 
nobilia  astrologua  ;  not  a  compliment  to  his  birth,  which  was 
humble,  but  to  his  fame.  The  suspension  was  because  : 

'  Sacree  Scriptures,  ejusque  verro  et  CatLolices  interpretation!  repug- 
nantia  (quod  in  horaine  Christiano  minime  tolerandum)  non  per  hypo- 
thesin  tractare,  sed  ut  verissima  adatruere  noa  dubitat  ! 

And  the  corrections  relate  : 

'  Locis  in  quibus^non  ex  hypothesi,  sed  asserendo  de  situ  et  motu  Terras 
disputat.' 

That  is,  the  earth's  motion  may  be  an  hypothesis  for  eluci- 
dation of  the  heavenly  motions,  but  must  not  be  asserted  as  a 
fact. 


(In  Pref.  circa  finem.)  '  Copernicus.  Si  fortasse  erunt 
qui  cum  omnium  Mathematum  ignari  sint,  tamen  de  illis  judicium  sibi 
summunt,  propter  aliquem  locum  scriptures,  male  ad  suum  propositum 
detortum,  ausi  fuerint  meum  hoc  institutum  reprehendere  ac  insec- 
tari  :  illos  nihil  moror  adeo  ut  etiam  illorum  judicium  tanquam 
temerarium  contemnam.  Non  enim  obscurum  est  Lactantium,  celebrem 
alioqui  scriptorem,  sed  Mathematicum  pai*um,  admodum  pueriliter  de 
forma  terree  loqui,  cum  deridet  eos,  qui  terrain  globi  formam  habere 
prodiderunt.  Itaque  non  debet  mirum  videri  stndiosis,  si  qui  tales  nos 
etiam  videbunt.  Mathemata  Mathematicis  scribuntur,  quibus  et  hi 
nostri  labores,  si  me  non  fallit  opinio,  videbuntur  etiam  Beipub.  eccle- 
siasticee  conducere  aliquid  .  .  .  Emend.  Ibi  si  fortasse  dele  omnia, 
usque  ad  verbum  hi  nostri  labores  et  sic  accommoda  —  Cceterum  hi  nostri 
labores.1 

All  the  allusion  to  Lactantius,  who  laughed  at  the  notion  of  the 
earth  being  round,  which  was  afterwards  found  true,  is  to  be 
struck  out. 

(Cap.  5.  lib.  i.  p.  8.)  '  Copernicus.  Si  tamen  attentius  rem  consider- 
emus,  videbitur  heec  queestio  nondum  absoluta,  et  idcirco  minime 
contemnenda.  Emend.  Si  tamen  attentius  rem  consideremus,  nihil 
refert  an  Terrain  in  medio  Mundi,  an  extra  Medium  existere,  quoad  sol- 
yendas  coelestium  motuum  apparentias  existimemus.' 

We  must  not  say  the  question  is  not  yet  settled,  but  only  that 


COPERNICUS  AND  THE  POPE.  59 

it  may  be  settled  either  way,  so  far  as  mere  explanation  of  the 
celestial  motions  is  concerned. 

(Cap.  8.  lib.  i.)  '  Totum  hoc  caput  potest  expungi,  quia  ex  professo 
tractat  de  veritate  motus  Terree,  dum  solvit  veterum  rationes  probantes 
ejus  quietem.  Cam  tamen  problematice  videatur  loqui ;  ut  studiosis 
satisfiat,  seriesque  et  ordo  libri  integer  maneat ;  emendetur  ut  infra.' 

A  chapter  which  seems  to  assert  the  motion  should  perhaps  be 
expunged  ;  but  it  may  perhaps  be  problematical ;  and,  not  to 
break  up  the  book,  must  be  amended  as  below. 

(p.  6.)  '  Ooperniciis.  Cui  ergo  hesitamus  adhuc,  nobilitatem  illi  formes 
sues  a  natura  congruentem  concedere,  magisquam  quod  totus  labatur 
mundus,  cujus  finis  ignoratur,  soirique  nequit,  neque  fateamur  ipsius 
cotidian®  revolutionis  in  coelo  apparentiam  esse,  et  in  terra  veritatem  ? 
Efc  heec  perinde  se  habere,  ac  si  diceret  Virgilianus  ^Eneas  :  Provehimur 
portu  ....  Emend.  Cur  ergo  non  possum  mobilitatem  illi  formsa 
sues  concedere,  magisque  quod  totus  labatur  mundus,  cujus  finis 
ignoratur  scirique  nequit,  et  quse  apparent  in  coelo,  perinde  se  habere, 
ao  si  .  .  .  .' 

'  Why  should  we  hesitate  to  allow  the  earth's  motion,'  must  be 
altered  into  '  I  cannot  concede  the  earth's  motion.' 

(p.  7.)  '  Copernicus.  Addo  etiam,  quod  satis  absurdum  videretur, 
continent!  sive  locanti  motnm  adscribi,  et  non  potius  contento  et 
locato,  quod  est  terra.  Emend.  Addo  etiam  difficilius  non  esse 
contento  et  locato,  quod  est  Terra,  motum  adscribere,  quam  continenti.' 

We  must  not  say  it  is  absurd  to  refuse  motion  to  the  contained 
and  located,  and  to  give  it  to  the  containing  and  locating ;  say 
that  neither  is  more  difficult  than  the  other. 

(p.  7.)  '  Copernicus.  Vides  ergo  quod  ex  his  omnibus  probabilior  sit 
mobilitas  Terras,  quam  ejus  quies,  preesertim  in  cotidiana  revolutione, 
tanquam  terne  maxime  propria.  EincmL  Vides  .  .  .  delendus  est 
usque  ad  finem  capitis.' 

Strike  out  the  whole  of  the  chapter  from  this  to  the  end ;  it 
says  that  the  motion  of  the  earth  is  the  most  probable  hypothesis. 

(Cap.  9.  lib.  i.  p.  7.)  '  Copernicus.  Cum  igitur  nihil  prohibeat  mobili- 
tatem Teme,  videndum  nunc  arbitror,  an  etiam  plures  illi  motua 
conveniant,  ut  possit  una  errantium  syderum  existimari.  Emend.  Cum 
igitur  Terram  moveri  assumpserim,  videndum  nunc  arbitror,  an  etiam 
illi  plures  possint  convenire  motus.' 

We  must  not  say  that  nothing  prohibits  the  motion  of  the 
earth,  only  that  having  assumed  it,  we  may  inquire  whether  our 
explanations  require  several  motions. 


60  A  BUDGET  OF  PARADOXES. 

(Cap.  10.  lib.  1.  p.  9.)  '  Copernicus.  Non  pudet  nosfateri  ....  hoc 
potius  in  mobilitate  terra?  verificari.  Emend.  ISTon  pudet  nos  assumere 
....  hoc  consequent er  in  mobilitate  verificari.' 

(Cap.  10.  lib.  i.  p.  10.)  '  Copernicus.  Tanta  nimiruni.  est  divina  ha3C 
Opt.  Max.  fabrica.  Emend.  Dele  ilia  verba  postrema.' 

(Cap.  ii.  lib.  i.)  '  Copernicus.  De  triplici  motu  telluris  demonstratio. 
Emend.  De  hypothesi  triplicis  motus  Terree,  ejusque  demonstratioiie.' 

(Cap.  10.  lib.  iv.  p.  122.)  '  Copernicus.  De  magnitudine  horum  trium 
siderum,  Solis,  Lunee,  et  Terrse.  Emend.  Dele  verba  horum  trium 
sidcrum,  quia  terra  non  est  sidus,  ut  facit  earn  Copernicus. ' 

We  must  not  say  we  are  not  ashamed  to  acknowledge ;  assume 
is  the  word.  We  must  not  call  this  assumption  a  Divine  work. 
A  chapter  must  not  be  headed  demonstration,  but  hypothesis. 
The  earth  must  not  be  called  a  star ;  the  word  implies  motion. 

It  will  be  seen  that  it  does  not  take  much  to  reduce  Copernicus 
to  pure  hypothesis.  No  personal  injury  being  done  to  the  author 
—  who  indeed  had  been  1 7  years  out  of  reach — the  treatment  of 
his  book  is  now  an  excellent  joke.  It  is  obvious  that  the  Car- 
dinals of  the  Index  were  a  little  ashamed  of  their  position,  and 
made  a  mere  excuse  of  a  few  corrections.  Their  mode  of  deal- 
ing with  chap.  8,  this problematice  videtur  loqui,ut  studiosis  satis- 
fiat,  is  an  excuse  to  avoid  corrections.  But  they  struck  out  the 
stinging  allusion  to  Lactantius  in  the  preface,  little  thinking, 
honest  men,  for  they  really  believed  what  they  said — that  the 
light  of  Lactantius  would  grow  dark  before  the  brightness  of 
their  own. 

1622.  I  make  no  reference  to  the  case  of  Galileo,  except  this. 
I  have  pointed  out  (Penny  Cycl.  Suppl.  '  Gralileo  ; '  Engl.  Cycl. 
'  Motion  of  the  Earth ')  that  it  is  clear  the  absurdity  was  the  act 
of  the  Italian  Inquisition — for  the  private  and  personal  pleasure 
of  the  Pope,  who  knew  that  the  course  he  took  would  not  commit 
him  as  Pope — and  not  of  the  body  which  calls  itself  the  Church. 
Let  the  dirty  proceeding  have  its  right  name.  The  Jesuit 
Riccioli,  the  stoutest  and  most  learned  Anti-Copernican  in 
Europe,  and  the  Puritan  Wilkins,  a  strong  Copernican  and 
Pope-hater,  are  equally  positive  that  the  Eoman  Church  never 
pronounced  any  decision  :  and  this  in  the  time  immediately  fol- 
lowing the  ridiculous  proceeding  of  the  Inquisition.  In  like 
manner  a  decision  of  the  Convocation  of  Oxford  is  not  a  law  of 
the  English  Church ;  which  is  fortunate,  for  that  Convocation, 
in  1622,  came  to  a  decision  quite  as  absurd,  and  a  great  deal 
more  wicked  than  the  declaration  against  the  motion  of  the  earth. 
The  second  was  a  foolish  mistake  :  the  first  was  a  disgusting 


KNIGHT  AND  THE  OXFORD  CONVOCATION.  61 

surrender  of  right  feeling.  Tbe  story  is  told  without  disappro- 
bation by  Anthony  Wood,  who  never  exaggerated  anything 
against  the  university  of  which  he  is  writing  eulogistic  history. 

In  1622,  one  William  Knight  put  forward  in  a  sermon  preached 
before  the  University  certain  theses  which,  looking  at  the  state 
of  the  times,  may  have  been  improper  and  possibly  of  seditious 
intent.  One  of  them  was  that  the  bishop  might  excommunicate 
the  civil  magistrate  :  this  proposition  the  clerical  body  could  not 
approve,  and  designated  it  by  the  term  erronea,  the  mildest 
going.  But  Knight  also  declared  as  follows — 

Stibditis  mere  privatis,  si  Tyrannus  tanquarn  latro  aut  stuprator 
in  ipsos  faciat  impetum,  et  ipsi  nee  potestatem  ordinariam 
implorare,  nee  alia  ratione  effugere  periculum  possint,  in  preserti 
periculo  se  et  suos  contra  tyrannum,  sicut  contra  privatum  gras- 
satorem,  defendere  licet. 

That  is,  a  man  may  defend  his  purse  or  a  woman  her  honour, 
against  the  personal  attack  of  a  king,  as  against  that  of  a  private 
person,  if  no  other  means  of  safety  can  be  found.  The  Convoca- 
tion sent  Knight  to  prison,  declared  the  proposition  'falsa, 
periculosa,  et  impiaj  and  enacted  that  all  applicants  for  degrees 
should  subscribe  this  censure,  and  make  oath  that  they  would 
neither  hold,  teach,  nor  defend  Knight's  opinions. 

The  thesis,  in  the  form  given,  was  unnecessary  and  improper. 
Though  strong  opinions  of  the  king's  rights  were  advanced  at  the 
time,  yet  no  one  ventured  to  say  that,  ministers  and  advisers 
apart,  the  king  might  personally  break  the  law ;  and  we  know 
that  the  first  and  only  attempt  which  his  successor  made  brought 
on  the  crisis  which  cost  him  his  throne  and  his  head.  But  the 
declaration  that  the  proposition  was  false  far  exceeds  in  all  that 
is  disreputable  the  decision  of  the  Inquisition  against  the  earth's 
motion.  We  do  not  mention  this  little  matter  in  England. 
Knight  was  a  Puritan,  and  Neal  gives  a  short  account  of  his  ser- 
mon. From  comparison  with  Wood,  I  judge  that  the  theses,  as 
given,  were  not  Knight's  words,  but  the  digest  which  it  was 
customary  to  make  in  criminal  proceedings  against  opinion. 
This  heightens  the  joke,  for  it  appears  that  the  qualifiers  of  the 
Convocation  took  pains  to  present  their  condemnation  of  Knight 
in  the  terms  which  would  most  unequivocally  make  their  censure 
condemn  themselves.  This  proceeding  took  place  in  the  interval 
between  the  two  proceedings  against  Gralileo  :  it  is  left  undeter- 
mined whether  we  must  say  pot-kettle-pot  or  kettle-pot-kettle. 


62  A  BUDGET   OF  PARADOXES. 

Liberti  Fromondi  .  .  '.  Ant-Aristarchus,  sive  orbis  terras  immo- 
bilis.  Antwerp,  1631,  8vo. 

This  book  contains  the  evidence  of  an  ardent  opponent  of 
Galileo  to  the  fact,  that  Eoman  Catholics  of  the  day  did  not  con- 
sider the  decree  of  the  Index  or  of  the  Inquisition  as  a  declara- 
tion of  their  Church.  Fromond  would  have  been  glad  to  say  as 
much,  and  tries  to  come  near  it,  but  confesses  he  must  abstain. 
See  Penny  Cyclop.  Suppl.  'Galileo,'  and  Eng.  Cycl.  'Motion 
of  the  Earth.'  The  author  of  a  celebrated  article  in  the  Dublin 
Review,  in  defence  of  the  Church  of  Eome,  seeing  that  Drink- 
water  Bethune  makes  use  of  the  authority  of  Fromondus,  but  for 
another  purpose,  sneers  at  him  for  bringing  up  a  '  musty  old  Pro- 
fessor.' If  he  had  known  Fromondus,  and  used  him  he  would  have 
helped  his  own  case,  which  is  very  meagre  for  want  of  knowledge.1 

Advis  a  Monseigneur  1'eminentissime  Cardinal  Due  de  Richelieu, 
siir  la  Proposition  faicte  par  le  Sieur  Morin  pour  1'invention  des 
longitudes.  Paris,  1634,  8vo. 

This  is  the  Official  Eeport  of  the  Commissioners  appointed  by 
the  Cardinal,  of  whom  Pascal  is  the  one  now  best  known,  to  consider 
Morin's  plan.  See  the  full  account  in  Delambre,  Hist.  Astr. 
Mod.  ii.  236,  &c. 

Arithmetica  et  Greometria  practica.  By  Adrian  Metius.  Ley- 
den,  1640,  4to. 

This  book  contains  the  celebrated  approximation  guessed  at  by 
his  father,  Peter  Metius,  namely,  that  the  diameter  is  to  the 
circumference  as  113  to  355.  The  error  is  at  the  rate  of  about  a 
foot  in  2,000  miles.  Peter  Metius,  having  his  attention  called 
to  the  subject  by  the  false  quadrature  of  Duchesne,  found  that 
the  ratio  lay  between  ^-5-  and  f|£.  He  then  took  the  liberty  of 
taking  the  mean  of  both  numerators  and  denominators,  giving 
44JJ-  He  had  no  right  to  presume  that  this  mean  was  better  than 
either  of  the  extremes ;  nor  does  it  appear  positively  that  he  did  so. 
He  published  nothing :  but  his  son  Adrian,  when  Van  Ceulen's  work 
showed  how  near  his  father's  result  came  to  the  truth,  first  made 
it  known  in  the  work  above.  (See  Eng.  Cyclop,  art. '  Quadrature.') 

A  discourse  concerning  a  new  world  and  another  planet,  in  two 

books.     London,  1640,  8vo. 
Cosmotheoros :    or  conjectures  concerning  the  planetary  worlds 

1  The  article  referred  to  is  about  thirty  years  old  :  since  it  appeared  another  has 
been  given  (Dubl.  Rev.  Sept.  1865)  which  is  of  much  greater  depth.  In  it  will  also  bo 
found  the  Roman  view  of  Bishop  Virgil  (ante,  p.  24). 


PLUEALITY   OF   WORLDS.  63 

and  their  inhabitants.  Written  in  Latin,  by  Christianus  Huy- 
ghens.  This  translation  was  first  published  in  1698.  Glasgow 
1757,  8vo.  [The  original  is  also  of  1698.] 

The  first  work  is  by  Bishop  Wilkins,  being  the  third  edition,  [first 
in  1638]  of  the  first  book,  'That  the  Moon  maybe  a  Planet;'  and  the 
first  edition  of  the  second  work,  '  That  the  Earth  may  be  a  Planet.' 
[See  more  under  the  reprint  of  1802.]  Whether  other  planets  be 
inhabited  or  not,  that  is,  crowded  with  organisations,  some  of 
them  having  consciousness,  is  not  for  me  to  decide ;  but  I  should 
be  much  surprised  if,  on  going  to  one  of  them,  I  should  find  it 
otherwise.  The  whole  dispute  tacitly  assumes  that,  if  the  stars 
and  planets  be  inhabited,  it  must  be  by  things  of  which  we  can 
form  some  idea.  But  for  aught  we  know,  what  number  of  such 
bodies  there  are,  so  many  organisms  may  there  be,  of  which  we 
have  no  way  of  thinking  nor  of  speaking.  This  is  seldom  re- 
membered. In  like  manner  it  is  usually  forgotten  that  the  matter 
of  other  planets  may  be  of  different  chemistry  from  ours.  There 
may  be  no  oxygen  and  hydrogen  in  Jupiter,  which  may  have  gens 
of  its  own.  But  this  must  not  be  said  :  it  would  limit  the  omni- 
science of  the  a  priori  school  of  physical  inquirers,  the  larger  half 
of  the  whole,  and  would  be  very  unphilosophical.  Nine-tenths 
of  my  best  paradoxers  come  out  from  among  this  larger  half, 
because  they  are  just  a  lit/tie  more  than  of  it  at  their  entrance. 

There  was  a  discussion  on  the  subject  some  years  ago,  which 
began  with — 

The  plurality  of  worlds  :  an  Essay.  London,  1853,  8vo.  [By  Dr. 
Wm.  Whewell,  Master  of  Trinity  College,  Cambridge].  A 
dialogue  on  the  plurality  of  worlds,  being  a  supplement  to  the 
Essay  on  that  subject.  [First  found  in  the  second  edition,  1854 ; 
removed  to  the  end  in  subsequent  editions,  and  separate  copies 
issued.] 

A  work  of  sceptical  character,  insisting  on  analogies  which  pro- 
hibit the  positive  conclusion  that  the  planets,  stars,  &c.,  are  what 
we  should  call  inhabited  worlds.  It  produced  several  works  and 
a  large  amount  of  controversy  in  reviews.  The  last  predecessor 
of  whom  I  know  was — 

Plurality  of  Worlds.  .   .  .  By  Alexander  Maxwell.  Second  Edition. 

London,  1820,  8vo. 

This  work  is  directed  against  the  plurality  by  an  author  who 
does  not  admit  modern  astronomy.  It  was  occasioned  by  Dr.  Chal- 
mers's celebrated  discourses  on  religion  in  connexion  with  astro- 
nomy. The  notes  contain  many  citations  on  the  gravity  controversy, 


64  A  BUDGET   OF  PAEADOXES. 

from  authors  now  very  little  read  :  and  this  is  its  present  value.  I 
find  no  mention  of  Maxwell,  not  even  in  Watt.  He  communicated 
with  mankind  without  the  medium  of  a  publisher ;  and,  from  Vieta 
till  now,  this  method  has  always  been  favourable  to  loss  of  books. 

A  correspondent  informs  me  that  Alex.  Maxwell,  who  wrote  on 
the  plurality  of  worlds,  in  1820,  was  a  law-bookseller  and  pub- 
lisher (probably  his  own  publisher)  in  Bell  Yard.  He  had  pecu- 
liar notions,  which  he  was  fond  of  discussing  with  his  customers. 
He  was  a  bit  of  a  Swedenborgian. 

There  is  a  class  of  hypothetical  creations  which  do  not  belong 
to  my  subject,  because  they  are  acknowledged  to  be  fictions,  as 
those  of  Lucian,  Eabelais,  Swift,  Francis  Godwin,  Voltaire,  &c. 
All  who  have  more  positive  notions  as  to  either  the  composition 
or  organisation  of  other  worlds,  than  the  reasonable  conclusion 
•that  our  Architect  must  be  quite  able  to  construct  millions  of 
other  buildings  on  millions  of  other  plans,  ought  to  rank  with 
the  writers  just  mentioned,  in  all  but  self-knowledge.  Of  every 
one  of  their  systems  I  say,  as  the  Irish  Bishop  said  of  Gulliver's 
book, — I  don't  believe  half  of  it.  Huyghens  had  been  preceded 
by  Fontenelle,  who  attracted  more  attention.  Huyghens  is  very 
fanciful  and  very  positive  ;  but  he  gives  a  true  account  of  his 
method.  '  But  since  there's  no  hopes  of  a  Mercury  to  carry  us 
such  a  journey,  we  shall  e'en  be  contented  with  what's  in  our 
power :  we  shall  suppose  ourselves  there.  .  .  .'  And  yet  he  says, 
— 'We  have  proved  that  they  live  in  societies,  have  hands  and 
feet.  .  .  .'  Kircher  had  gone  to  the  stars  before  him,  but  would 
not  find  any  life  in  them,  either  animal  or  vegetable. 

The  question  of  the  inhabitants  of  a  particular  planet  is  one 
which  has  truth  on  one  side  or  the  other  :  either  there  are  some 
inhabitants,  or  there  are  none.  Fortunately,  it  is  of  no  conse- 
quence which  is  true.  But  there  are  many  cases,  where  the 
balance  is  equally  one  of  truth  and  falsehood,  in  which  the  choice 
is  a  matter  of  importance.  My  work  selects,  for  the  most  part, 
sins  against  demonstration  :  but  the  world  is  full  of  questions  of 
fact  or  opinion,  in  which  a  struggling  minority  will  become  a 
majority,  or  else  will  be  gradually  annihilated  :  and  each  of  the 
cases  subdivides  into  results  of  good,  and  results  of  evil.  What  is 
to  be  done  ? 

Periculosum  est  credere  et  non  credere ; 
Hippolitus  obiit  quia  novercee  creditum  est ; 
Cassandrse  quia  non  creditum  ruit  Ilium  : 
Ergo  exploranda  est  veritas  multum  prius 
Quam  stulta  prove  judicet  sententia. 


VENETIAN  PAKADOXERS.   LONGOMONTANUS.        65 


Nova  Demonstratio  immobilitatis  terraB  petita  ex  virtute  mag- 
netica.  Bj  Jacobus  Grandamicus.  Flcxiae  (La  Fleche),  1645, 
4*o. 

No  magnetic  body  can  move  about  its  poles :  the  earth  is  a 
magnetic  body,  therefore,  &c.  The  iron  and  its  magnetism  are 
typical  of  two  natures  in  one  person  ;  so  it  is  said,  '  Si  exaltatus 
fuero  a  terra,  omnia  traham  ad  me  ipsum.' 

Le  glorie  degli  incogniti,  o  vero  gli  huomini  illustri  dell'  ac- 
cademia  de'  signer!  incogniti  di  Venetia.  Venice,  1 647,  4to. 

This  work  is  somewhat  like  a  part  of  my  own  :  it  is  a  budget 
of  Venetian  nobodies  who  wished  to  be  somebodies  ;  but  paradox 
is  not  the  only  means  employed.  It  is  of  a  serio-comic  character, 
gives  genuine  portraits  in  copper-plate,  and  grave  lists  of  works ; 
but  satirical  accounts.  The  astrologer  Andrew  Argoli  is  there, 
and  his  son  ;  both  of  whom,  with  some  of  the  others,  have  place  in 
modern  works  on  biography.  Argoli's  discovery  that  logarithms 
facilitate  easy  processes,  but  increase  the  labour  of  difficult  ones, 
is  worth  recording. 

Controversiae   de  vera   circuli   mensura  .  .  .    inter 

C.  S.  Longomontanum  et  Jo.  Pellium.    Amsterdam,  1647,  4to. 

Longomontanus,  a  Danish  astronomer  of  merit,  squared  the 
circle  in  1644  :  he  found  out  that  the  diameter  43  gives  the  square 
root  of  18252  for  the  circumference;  which  gives  3*14185  .  .  . 
for  the  ratio.  Pell  answered  him,  and  being  a  kind  of  circulating 
medium,  managed  to  engage  in  the  controversy  names  known  and 
unknown,  as  Koberval,  Hobbes,  Carcavi,  Lord  Charles  Cavendish, 
Pallieur,  Mersenne,  Tassius,  Baron  Wolzogen,  Descartes,  Cavalieri 
and  Grolius.  Among  them,  of  course,  Longomontanus  was  made 
mincemeat :  but  he  is  said  to  have  insisted  on  the  discovery  in  his 
epitaph. 

The  great  circulating  mediums,  who  wrote  to  everybody,  heard 
from  everybody,  and  sent  extracts  to  everybody  else,  have  been 
Father  Mersenne,  John  Collins,  and  the  late  Prof.  Schumacher : 
all  'late'  no  doubt,  but  only  the  last  recent  enough  to  be  so 
styled.  If  M.C.S.  should  ever  again  stand  for  '  Member  of  the 
Corresponding  Society,'  it  should  raise  an  acrostic  thought  of  the 
three.  There  is  an  allusion  to  Mersenne's  occupation  in  Hobbes's 
reply  to  him.  He  wanted  to  give  Hobbes,  who  was  very  ill  at 
Paris,  the  Roman  Eucharist :  but  Hobbes  said,  'I  have  settled  all 

F 


QQ  A  BUDGET   OF  PARADOXES. 

that  long  ago ;  when  did  you  hear  from  Grassendi  ?'  We  are  re- 
minded of  William's  answer  to  Burnet.  John  Collins  disseminated 
Newton,  among  others.  Schumacher  ought  to  have  been  called 
the  postmaster-general  of  astromony,  as  Collins  was  called  the 
attorney-general  of  mathematics. 

A  late  discourse.  ...  by  Sir  Kenelme  Digby  .  .  .  Rendered  into 
English  by  R.  White.     London,  1658,  12mo. 

On  this  work  see  Notes  and  Queries,  2nd  series,  vii.  231,  299, 
445,  viii.  190.  It  contains  the  celebrated  sympathetic  powder.  I 
am  still  in  much  doubt  as  to  the  connexion  of  Digby  with  this 
tract.  Without  entering  on  the  subject  here,  I  observe  that  in 
Birch's  'History  of  the  Royal  Society,'  to  which  both  Digby  and 
White  belonged,  Digby,  though  he  brought  many  things  before 
the  Society,  never  mentioned  the  powder,  which  is  connected  only 
with  the  names  of  Evelyn  and  Sir  Gilbert  Talbot.  The  sym- 
pathetic powder  was  that  which  cured  by  anointing  the  weapon 
with  its  salve  instead  of  the  wound.  I  have  long  been  convinced 
that  it  was  efficacious.  The  directions  were  to  keep  the  wound 
clean  and  cool,  and  to  take  care  of  diet,  rubbing  the  salve  on  the 
knife  or  sword.  If  we  remember  the  dreadful  notions  upon  drugs 
which  prevailed,  both  as  to  quantity  and  quality,  we  shall  readily 
see  that  any  way  of  not  dressing  the  wound  would  have  been  use- 
ful. If  the  physicians  had  taken  the  hint,  had  been  careful  of 
diet,  &c. ,  and  had  poured  the  little  barrels  of  medicine  down  the 
throat  of  a  practicable  doll,  they  would  have  had  their  magical 
cures  as  well  as  the  surgeons.  Matters  are  much  improved  now  ; 
the  quantity  of  medicine  given,  even  by  orthodox  physicians, 
would  have  been  called  infinitesimal  by  their  professional  ances- 
tors. Accordingly,  the  College  of  Physicians  has  a  right  to 
abandon  its  motto,  which  is  Ars  longa,  vita  brevis,  meaning 
Practice  is  long,  so  life  is  short. 

Examinatio  et  emendatio  Mathematics  Hodiernse.     By  Thomas 
Hobbes.     London.  1666,  4to. 

In  six  dialogues  :  the  sixth  contains  a  quadrature  of  the  circle. 
But  there  is  another  edition  of  this  work,  without  place  or  date 
on  the  title-page,  in  which  the  quadrature  is  omitted.  This 
seems  to  be  connected  with  the  publication  of  another  quadra- 
ture, without  date,  but  about  1670,  as  may  be  judged  from  its 
professing  to  answer  a  tract  of  Wallis,  printed  in  1669.  The 
title  is  '  Quadratura  circuli,  cubatio  sphaBroe,  duplicatio  cubi,'  4to . 


THOMAS   HOBBES.      SCALIGER.  67 

Hobbes,  who  began  in  1655,  was  very  wrong  in  his  quadrature  ; 
but,  though  not  a  Gregory  St.  Vincent,  he  was  not  the  ignoramus 
in  geometry  that  he  is  sometimes  supposed.  His  writings,  erro- 
neous as  they  are  in  many  things,  contain  acute  remarks  on  points 
of  principle.  He  is  wronged  by  being  coupled  with  Joseph 
Scaliger,  as  the  two  great  instances  of  men  of  letters  who  have 
come  into  geometry  to  help  the  mathematicians  out  of  their  diffi- 
culty. I  have  never  seen  Scaliger's  quadrature,  except  in  the 
answers  of  Adrianus  Eomanus,  Vieta  and  Clavius,  and  in  the 
extracts  of  Kastner.  Scaliger  had  no  right  to  such  strong  oppo- 
nents :  Erasmus  or  Bentley  might  just  as  well  have  tried  the 
problem,  and  either  would  have  done  much  better  in  any  twenty 
minutes  of  his  life. 

Scaliger  inspired  some  mathematicians  with  great  respect  for 
his  geometrical  knowledge.  Vieta,  the  first  man  of  his  time,  who 
answered  him,  had  such  regard  for  his  opponent  as  made  him 
conceal  Scaliger's  name.  Not  that  he  is  very  respectful  in  his 
manner  of  proceeding  :  the  following  dry  quiz  on  his  opponent's 
logic  must  have  been  very  cutting,  being  true.  '  In  grammaticis, 
dare  navibus  Austros,  et  dare  naves  Austris,  sunt  aeque  significantia. 
Sed  in  Geometricis,  aliud  est  adsumpsisse  circulum  BCD  non  esse 
majorem  triginta  sex  segmentis  BCDF,  aliud  circulo  BCD  non  esse 
majora  trigiuta  sex  segmenta  BCDF.  Ilia  adsumptiuncula  vera  est^ 
hoec  falsa.'  Isaac  Casaubon,  in  one  of  his  letters  to  De  Thou, 
relates  that,  he  and  another  paying  a  visit  to  Vieta,  the  conversa- 
tion fell  upon  Scaliger,  of  whom  the  host  said  that  he  believed 
Scaliger  was  the  only  man  who  perfectly  understood  mathematical 
writers,  especially  the  Greek  ones  :  and  that  he  thought  more  of 
Scaliger  when  wrong  than  of  many  others  when  right  ;  pluris  se 
Scaligerum  vel  errantem  facere  quam  multos  KaropSovvras.  This 
must  have  been  before  Scaliger's  quadrature  (1594).  There  is  an 
old  story  of  some  one  saying, '  Mallem  cum  Scaligero  errare,  quam 
cum  Clavio  recte  sapere.'  This  I  cannot  help  suspecting  to  have 
been  a  version  of  Vieta's  speech  with  Clavius  satirically  inserted, 
on  account  of  the  great  hostility  which  Vieta  showed  towards 
Clavius  in  the  latter  years  of  his  life. 

Montucla  could  not  have  read  with  care  either  Scaliger's  quadra- 
ture or  Clavius's  refutation.  He  gives  the  first  a  wrong  date  :  he 
assures  the  world  that  there  is  no  question  about  Scaliger's  quad- 
rature being  wrong,  in  the  eyes  of  geometers  at  least :  and  he 
states  that  Clavius  mortified  him  extremely  by  showing  that  it 
made  the  circle  less  than  its  inscribed  dodecagon,  which  is,  of 
course,  equivalent  to  asserting  that  a  straight  line  is  not  always 

F   2 


68  A  BUDGET   OF  PARADOXES. 

the  shortest  distance  between  two  points.  Did  Clavius  show 
this  ?  No,  it  was  Scaliger  himself  who  showed  it,  boasted 
of  it,  and  declared  it  to  be  a  '  noble  paradox '  that  a  theorem 
false  in  geometry  is  true  in  arithmetic  ;  a  thing,  he  says  with 
great  triumph,  not  noticed  by  Archimedes  himself!  He  says  in 
so  many  words  that  the  periphery  of  the  dodecagon  is  greater 
than  that  of  the  circle  ;  and  that  the  more  sides  there  are  to  the 
inscribed  figure,  the  more  does  it  exceed  the  circle  in  which  it  is. 
And  here  are  the  words,  on  the  independent  testimonies  of  Clavius 
and  Kastner : — 

Ambitus  dodecagon!  circulo  inscribendi  plus  potest  quam  circuli  am- 
bitus. Et  quanto  deinceps  pluriuin  laterum  fuerit  polygonum  circulo 
inscribendum,  tanto  plus  poterit  ambitus  polygoni  quam  ambitus 
circuli. 

There  is  much  resemblance  between  Joseph  Scaliger  and 
William  Hamilton,  in  a  certain  impetuosity  of  character,  and  in- 
aptitude to  think  of  quantity.  Scaliger  maintained  that  the  arc 
of  a  circle  is  less  than  its  chord  in  arithmetic,  though  greater  in 
geometry  ;  Hamilton  arrived  at  two  quantities  which  are  identi- 
cal, but  the  greater  the  one  the  less  the  other.  But,  on  the  whole, 
I  liken  Hamilton  rather  to  Julius  than  to  Joseph.  On  this  last 
hero  of  literature  I  repeat  Thomas  Edwards,  who  says  that  a  man 
is  unlearned  who,  be  his  other  knowledge  what  it  may,  does  not 
understand  the  subject  he  writes  about.  And  now  one  of  many 
instances  in  which  literature  gives  to  literature  character  in 
science.  Anthony  Teissier,  the  learned  annotator  of  De  Thou's 
biographies,  says  of  Finseus,  '  II  se  vanta  sans  raison  avoir  trouve 
la  quadrature  du  cercle  ;  la  gloire  de  cette  admirable  decouverte 
etait  reservee  a  Joseph  Scaliger,  comme  1'a  ecrit  Scevole  de 
St.  Marthe.' 

Natural  and  Political  Observations  .  .  .  npon  the  Bills  of 
Mortality.  By  John  Graunt,  citizen  of  London.  London,  1662, 
4to. 

This  is  a  celebrated  book,  the  first  great  work  upon  mortality. 
But  the  author,  going  ultra  crepidam,  has  attributed  to  the 
motion  of  the  moon  in  her  orbit  all  the  tremors  which  she  gets 
from  a  shaky  telescope.  But  there  is  another  paradox  about  this 
book  :  the  above  absurd  opinion  is  attributed  to  that  excellent 
mechanist,  Sir  William  Petty,  who  passed  his  days  among  the 
astronomers.  Orraunt  did  not  write  his  own  book  I  Anthony  Wood 
hints  that  Petty  '  assisted,  or  put  into  a  way '  his  old  benefactor : 
no  doubt  the  two  friends  talked  the  matter  over  many  a  time. 


JOHN  GEAUNT.   GADBURY  ON  COMETS.         69 

Burnet  and  Pepys  state  that  Petty  wrote  the  book.  It  is  enough 
for  me  that  Graunt,  whose  honesty  was  never  impeached,  uses  the 
plainest  incidental  professions  of  authorship  throughout ;  that  he 
was  elected  into  the  Eoyal  Society  because  he  was  the  author ; 
that  Petty  refers  to  him  as  author  in  scores  of  places,  and  published 
an  edition,  as  editor,  after  Graunt's  death,  with  Graunt's  name  of 
course.  The  note  on  Graunt  in  the  '  Biographia  Britannica '  may 
be  consulted ;  it  seems  to  me  decisive.  Mr.  C.  B.  Hodge,  an  able 
actuary,  has  done  the  best  that  can  be  done  on  the  other  side  in  the 
Assurance  Magazine,  viii.  234.  If  I  may  say  what  is  in  my  mind, 
without  imputation  of  disrespect,  I  suspect  some  actuaries  have 
a  bias :  they  would  rather  have  Petty  the  greater  for  their  Cory- 
pha3us  than  Graunt  the  less. 

Pepys  is  an  ordinary  gossip :  but  Burnet's  account  has  an  ani- 
mus which  is  of  a  worse  kind.  He  talks  of  '  one  Grraunt,  a  Papist, 
under  whose  name  Sir  William  Petty  published  his  observations 
on  the  bills  of  mortality.'  He  then  gives  the  cock  without  a  bull 
story  of  Graunt  being  a  trustee  of  the  New  River  Company,  and 
shutting  up  the  cocks  and  carrying  off  their  keys,  just  before  the 
fire  of  London,  by  which  a  supply  of  water  was  delayed.  It  was 
one  of  the  first  objections  made  to  Burnet's  work,  that  Graunt  was 
not  a  trustee  at  the  time  ;  and  Maitland,  the  historian  of  London, 
ascertained  from  the  books  of  the  Company  that  he  was  not 
admitted  until  twenty-three  days  after  the  breaking  out  of  the 
fire.  Graunt's  first  admission  to  the  Company  took  place  on  the 
very  day  on  which  a  committee  was  appointed  to  inquire  into  the 
cause  of  the  fire.  So  much  for  Burnet.  I  incline  to  the  view  that 
Graunt's  setting  London  on  fire  strongly  corroborates  his  having 
written  on  the  bills  of  mortality  :  every  practical  man  takes  stock 
before  he  commences  a  grand  operation  in  business. 

De  Cometis :  or  a  discourse  of  the  natures  and  effects  of 
Comets,  as  they  are  philosophically,  historically,  and  astrologi- 
cal^ considered.  With  a  brief  (yet  full)  account  of  the  III  late 
Comets,  or  blazing  stars,  visible  to  all  Europe.  And  what  (in  a 
natural  way  of  judicature)  they  portend.  Together  with  some 
observations  on  the  nativity  of  the  Grand  Seignior.  By  John 
Gadbury,  ^iXo^a^qyuartk-o'c.  London,  1665,  4to. 

Gadbury,  though  his  name  descends  only  in  astrology,  was  a  well- 
informed  astronomer.  D'Israeli  sets  down  Gadbury,  Lilly,  Wharton, 
Booker,  &c.,  as  rank  rogues  :  I  think  him  quite  wrong.  The  easy 
belief  in  roguery  and  intentional  imposture  which  prevails  in 
edueated  society  is,  to  my  mind,  a  greater  presumption  against  the 


70  A  BUDGET   OF  PARADOXES. 

honesty  of  mankind  than  all  the  roguery  and  imposture  itself. 
Putting  aside  mere  swindling  for  the  sake  of  gain,  and  looking  at 
speculation  and  paradox,  I  find  very  little  reason  to  suspect  wilful 
deceit.  My  opinion  of  mankind  is  founded  upon  the  mournful  fact 
that,  so  far  as  I  can  see,  they  find  within  themselves  the  means  of 
believing  in  a  thousand  times  as  much  as  there  is  to  believe  in, 
judging  by  experience.  I  do  not  say  anything  against  Isaac 
D'Israeli  for  talking  his  time.  We  are  all  in  the  team,  and  we  all 
go  the  road,  but  we  do  not  all  draw. 

An  essay  towards  a  real  character  and  a  philosophical  language. 
By  John  Wilkins  [Dean  of  Ripon,  afterwards  Bishop  of 
Chester].  London,  1668,  folio. 

This  work  is  celebrated,  but  little  known.  Its  object  gives  it 
a  right  to  a  place  among  paradoxes.  It  proposes  a  language — if 
that  be  the  proper  name — in  which  things  and  their  relations 
shall  be  denoted  by  signs,  not  words :  so  that  any  person,  what- 
ever may  be  his  mother  tongue,  may  read  it  in  his  own  words. 
This  is  an  obvious  possibility,  and,  I  am  afraid,  an  obvious  im- 
practicability. One  man  may  construct  such  a  system — Bishop 
Wilkins  has  done  it — but  where  is  the  man  who  will  learn  it  ? 
The  second  tongue  makes  a  language,  as  the  second  blow  makes  a 
fray.  There  has  been  very  little  curiosity  about  his  performance, 
the  work  is  scarce  ;  and  I  do  not  know  where  to  refer  the  reader  for 
any  account  of  its  details,  except  to  the  partial  reprint  of  Wilkins 
presently  mentioned  under  1802,  in  which  there  is  an  unsatisfac- 
tory abstract.  There  is  nothing  in  the  '  Biographia  Britannica,' 
except  discussion  of  Anthony  Wood's  statement  that  the  hint  was 
derived  from  Dalgarno's  book,  '  De  Signis,'  1661.  Hamilton 
('  Discussions,'  Art.  5,'  Dalgarno ')  does  not  say  a  word  on  this  point, 
beyond  quoting  Wood  ;  and  Hamilton,  though  he  did  now  and 
then  write  about  his  countrymen  with  a  rough-nibbed  pen,  knew 
perfectly  well  how  to  protect  their  priorities. 

Problema  Austriacum.     Plus  ultra  Quadratura  Circuli.     Auctore 
-  P.   Gregorio  a   Sancto  Vincentio  Soc.    Jesu.,   Antwerp,  1647, 
folio. — Opus  Geometricum  posthumum  ad  Mesolabium.     By  the 
same.     Gandavi  [Ghent],  1668,  folio. 

The  first  book  has  more  than  1200  pages,  on  all  kinds  of 
geometry.  Gregory  St.  Vincent  is  the  greatest  of  circle-squarers, 
and  his  investigations  led  him  into  many  truths  :  he  found  the 
property  of  the  area  of  the  hyperbola  which  led  to  Napier's  loga- 
rithms being  called  hyperbolic.  Montucla  says  of  him,  with  sly 


THE  MESOLABUM.      GEOMETRICAL   QUADRATURE.  71 

truth,  that  no  one  has  ever  squared  the  circle  with  so  much  genius, 
or,  excepting  his  principal  object,  with  so  much  success.  His 
reputation,  and  the  many  merits  of  his  work,  led  to  a  sharp  con- 
troversy on  his  quadrature,  which  ended  in  its  complete  exposure 
by  Huyghens  and  others.  He  had  a  small  school  of  followers, 
who  defended  him  in  print. 

Renati  Francisci  Slusii  Hesolabum.  Leodii  Eburonum  [Liege], 
1668,  4to. 

The  Mesolabum  is  the  solution  of  the  problem  of  finding  two 
mean  proportionals,  which  Euclid's  geometry  does  not  attain. 
Slusius  is  a  true  geometer,  and  uses  the  ellipse,  &c.:  but  he  is 
sometimes  ranked  with  the  trisectors,  for  which  reason  I  place  him 
here,  with  this  explanation. 

The  finding  of  two  mean  proportionals  is  the  preliminary  to  the 
famous  old  problem  of  the  duplication  of  the  cube,  proposed  by 
Apollo  (not  Apollonius)  himself.  D'Israeli  speaks  of  the  '  six 
follies  of  science,' — the  quadrature,  the  duplication,  the  perpetual 
motion,  the  philosopher's  stone,  magic,  and  astrology.  He  might 
as  well  have  added  the  trisection,  to  make  the  mystic  number  seven  : 
but  had  he  done  so,  he  would  still  have  been  very  lenient ;  only 
seven  follies  in  all  science,  from  mathematics  to  chemistry ! 
Science  might  have  said  to  such  a  judge — as  convicts  used  to  say 
who  got  seven  years,  expecting  it  for  life,  '  Thank  you,  my  Lord, 
and  may  you  sit  there  till  they  are  over,' — may  the  Curiosities  of 
Literature  outlive  the  Follies  of  Science ! 

1668.  In  this  year  James  Gregory,  in  his  Vera  Circuli  et 
Hyperbolce  Quadratura,  held  himself  to  have  proved  that  the 
geometrical  quadrature  of  the  circle  is  impossible.  Few  mathe- 
maticians read  this  very  abstruse  speculation,  and  opinion  is 
somewhat  divided.  The  regular  circle-squarers  attempt  the 
arithmetical  quadrature,  which  has  long  been  proved  to  be  impos- 
sible. Very  few  attempt  the  geometrical  quadrature.  One  of 
the  last  is  Malacarne,  an  Italian,  who  published  his  Solution 
Geometrique,  at  Paris,  in  1825.  His  method  would  make  the 
circumference  less  than  three  times  the  diameter. 

La  Geomeh-ie  Frai^oise,  ou  la  Pratique  aisee  ...  La  quadracture 
du  cercle.  Par  le  Sieur  de  Beaulieu,  Ingenieur,  Geographe  du 
Boi  .  .  .  Paris,  1676,  8vo.  [not  Poutault  de  Beaulieu,  the  cele- 
brated topographer  ;  he  died  in  1674]. 

If  this  book  had  been  a  fair  specimen,  I  might  have  pointed 
to  it  in  connection  with  contemporary  English  works,  and  made 


72  A  BUDGET  OF  PAKADOXES. 

a  scornful  comparison.  But  it  is  not  a  fair  specimen.  Beaulieu 
was  attached  to  the  Eoyal  Household,  and  throughout  the  century 
it  may  be  suspected  that  the  household  forced  a  royal  road  to 
geometry.  Fifty  years  before,  Beaugrand,  the  king's  secretary, 
made  a  fool  of  himself,  and  [so  ?]  contrived  to  pass  for  a  geometer. 
He  had  interest  enough  to  get  Desargues,  the  most  powerful 
geometer  of  his  time,  the  teacher  and  friend  of  Pascal,  prohibited 
from  lecturing.  See  some  letters  on  the  History  of  Perspective, 
which  I  wrote  in  the  Athenceum,  in  October  and  November, 
1861.  Montucla,  who  does  not  seem  to  know  the  true  secret  of 
Beaugrand's  greatness,  describes  him  as  '  un  certain  M.  de  Beau- 
grand,  mathematicien,  fort  mal  traite  par  Descartes,  et  a  ce  qu'il 
paroit  avec  justice.' 

Beaulieu's  quadrature  amounts  to  a  geometrical  construction 
which  gives  ?r=  V'lO.  His  depth  may  be  ascertained  from  the 
following  extracts.  First,  on  Copernicus  : — 

Copernic,  Allenaand,  ne  s'esfc  pas  moins  rendu  illustre  par  ses  doctes 
ecrits  ;  et  nous  pourrions  dire  de  luy,  qu'il  seroit  le  seul  et  unique  en 
la  force  de  ses  Problemes,  si  sa  trop  grande  presomption  ne  1'avoit 
porte  a  avancer  en  cette  Science  une  proposition  aussi  absurde,  qu'elle 
est  centre  la  Foy  et  raison,  en  faisant  la  circonference  d'un  Cercle  fixe, 
immobile,  et  le  centre  mobile,  sur  lequel  principe  Geometrique,  il  a 
avance  en  son  Traitte  Astrologique  le  Soleil  fixe,  et  la  Terre  mobile. 

I  digress  here  to  point  out  that  though  our  quadrators,  &c., 
very  often,  and  our  historians  sometimes,  assert  that  men  of  the 
character  of  Copernicus,  &c.  were  treated  with  contempt  and 
abuse  until  their  day  of  ascendancy  came,  nothing  can  be  more 
incorrect.  From  Tycho  Brahe  to  Beaulieu,  there  is  but  one 
expression  of  admiration  for  the  genius  of  Copernicus.  There  is 
an  exception,  which,  I  believe,  has  been  quite  misunderstood. 
Maurolycus,  in  his  'De  Sphaera,'  written  many  years  before  its 
posthumous  publication  in  1575,  and  which  it  is  not  certain  he 
would  have  published,  speaking  of  the  safety  with  which  various 
authors  may  be  read  after  his  cautions,  says,  '  Toleratur  et 
Nicolaus  Copernicus  qui  Solem  fixum  et  Terrain  in  girum 
circumverti  posuit :  et  scutica  potius,  aut  flagello,  quam  repre- 
hensione  dignus  est.'  Maurolycus  was  a  mild  and  somewhat 
contemptuous  satirist,  when  expressing  disapproval :  as  we  should 
now  say,  he  pooh-poohed  his  opponents  ;  but,  unless  the  above 
be  an  instance,  he  was  never  savage  nor  impetuous.  I  am  fully 
satisfied  that  the  meaning  of  the  sentence  is,  that  Copernicus, 
who  turned  the  earth  like  a  boy's  top,  ought  rather  to  have  a  whip 
given  him  wherewith  to  keep  up  his  plaything  than  a  serious 


BEAULIEU'S   ALGEBRA.      SIR  M.  HALE.  73 

refutation.     To  speak  of  tolerating  a  person  as  being  more  worthy 
of  a  flogging  than  an  argument,  is  almost  a  contradiction. 
I  will  now  extract  Beaulieu's  treatise  on  algebra,  entire. 

L'Algebre  est  la  science  curieuse  des  S9avans  et  specialement  d'un 
General  d'Armee  on  Capitaine,  pour  promptement  ranger  une  Armee 
en  bataille,  et  nombre  de  Mousquetaires  et  Piquiers  qui  composent  les 
bataillons  d'icelle,  outre  les  figures  de  I'Arithmetique.  Cette  science  a 
5  figures  particulieres  en  cette  sorte.  P  signifie  plus  au  commerce,  et 
a  1'Armee  Piquiers.  M  signifie  moins,  et  Mousquetaire  en  1'Art  dcs 
bataillons.  [It  is  quite  true  that  P  and  M  were  used  for  plus  and  minus 
in  a  great  many  old  works.]  R  signifie  ratine  en  la  mesure  du  Cube, 
et  en  1'Armee  rang.  Q  signifie  quare  en  Tun  et  1'autre  usage.  C 
signifie  cube  en  la  mesure,  et  Cavallerie  en  la  composition  des  bataillons 
et  escadrons.  Quant  a  1'operation  de  cette  science,  c'est  d'additionner 
un  plus  d'avec  plus,  la  somme  sera  plus,  et  moins  d'avec  plus,  on 
soustrait  le  moindre  du  plus,  etlareste  est  la  somme  requise  ou  nombre 
trouve.  Je  dis  seulement  cecy  en  passant  pour  ceux  qui  n'en  S9avent 
rien  du  tout. 

This  is  the  algebra  of  the  Koyal  Household,  seventy-three  years 
after  the  death  of  Vieta.  Quaere,  is  it  possible  that  the  fame  of 
Vieta,  who  himself  held  very  high  stations  in  the  household  all 
his  life,  could  have  given  people  the  notion  that  when  such  an 
officer  chose  to  declare  himself  an  algebraist,  he  must  be  one 
indeed  ?  This  would  explain  Beaugrand,  Beaulieu,  and  all  the 
beaux.  Beaugrand — not  only  secretary  to  the  king,  but  '  mathe- 
matician '  to  the  Duke  of  Orleans — I  wonder  what  his  'fool 'could 
have  been  like,  if  indeed  he  kept  the  offices  separate, — would 
have  been  in  my  list  if  I  had  possessed  his  Geostatique,  pub- 
lished about  1638.  He  makes  bodies  diminish  in  weight  as  they 
approach  the  earth,  because  the  effect  of  a  weight  on  a  lever  is 
less  as  it  approaches  the  fulcrum. 

Remarks  upon  two  late  ingenious  discourses  .  .  .  By  Dr.  Henry 
More.     London,  1676,  8vo. 

In  1673  and  1675,  Matthew  Hale,  then  Chief  Justice,  published 
two  tracts,  an  '  Essay  touching  Gravitation,'  and  '  Difficiles  Nuga?' 
on  the  Torricellian  experiment.  Here  are  the  answers  by  the 
learned  and  voluminous  Henry  More.  The  whole  would  be 
useful  to  any  one  engaged  in  research  about  ante-Newtonian 
notions  of  gravitation. 


74  A    BUDGET   OF  PABADOXES. 


Observations  touching  the  principles  of  natural  motions  ;  and 
especially  touching  rarefaction  and  condensation  .  .  .  By  the 
author  of  Difficiles  Nugce.  London,  1677,  8vo. 

This  is  another  tract  of  Chief  Justice  Hale,  published  the  year 
after  his  death.  The  reader  will  remember  that  motion,  in  old 
philosophy,  meant  any  change  from  state  to  state  :  what  we  now 
describe  as  motion  was  local  motion.  This  is  a  very  philosophical 
book,  about  flux  and  materia  prima,  virtus  activa  and  essentialis, 
and  other  fundamentals.  I  think  Stephen  Hales,  the  author  of 
the  '  Vegetable  Statics,'  has  the  writings  of  the  Chief  Justice 
sometimes  attributed  to  him,  which  is  very  puny  justice  indeed. 
Matthew  Hale  died  in  1676,  and  from  his  devotion  to  science  it 
probably  arose  that  his  famous  Pleas  of  the  Crown  and  other  law 
works  did  not  appear  until  after  his  death.  One  of  his  con- 
temporaries was  the  astronomer  Thomas  Street,  whose  Caroline 
Tables  were  several  times  printed  :  another  contemporary  was 
his  brother  judge,  Sir  Thomas  Street.  But  of  the  astronomer 
absolutely  nothing  is  known :  it  is  very  unlikely  that  he  and  the 
judge  were  the  same  person,  but  there  is  not  a  bit  of  positive  evi- 
dence either  for  or  against,  so  far  as  can  be  ascertained.  Halley — 
no  less  a  person — published  two  editions  of  the  'Caroline  Tables,'  no 
doubt  after  the  death  of  the  author :  strange  indeed  that  neither 
Halley  nor  any  one  else  should  leave  evidence  that  Street  was 
born  or  died. 

Matthew  Hale  gave  rise  to  an  instance  of  the  lengths  a  lawyer 
will  go  when  before  a  jury  who  cannot  detect  him.  Sir  Samuel 
Shepherd,  the  Attorney  General,  in  opening  Hone's  first  trial, 
calls  him  '  one  who  was  the  most  learned  man  that  ever  adorned 
the  Bench,  the  most  even  man  that  ever  blessed  domestic  life,  the 
most  eminent  man  that  ever  advanced  the  progress  of  science, 
and  one  of  the  [very  moderate]  best  and  most  purely  religious 
men  that  ever  lived. 

Basil  Valentine  his  triumphant  Chariot  of  Antimony,  with 
annotations  of  Theodore  Kirkringius,  M.D.  With  the  true  book 
of  the  learned  Synesius,  a  Greek  abbot,  taken  out  of  the 
Emperour's  library,  concerning  the  Philosopher's  Stone. 
London,  1678,  8vo. 

There  are  said  to  be  three  Hamburg  editions  of  the  collected 
works  of  Valentine,  who  discovered  the  common  antimony,  and 
is  said  to  have  given  the  name  antimoine,  in  a  curious  way. 
Finding  that  the  pigs  of  his  convent  throve  upon  it,  he  gave  it 


BASIL  VALENTINE.      THE  ALCHEMISTS.  75 

to  his  brethren,  who  died  of  it.  The  impulse  given  to  chemistry 
by  E.  Boyle  seems  to  have  brought  out  a  vast  number  of  transla- 
tions, as  in  the  following  tract  :  — 

Collectanea  Chymica  :  A  collection  of  ten  several  treatises  in 
chymistry,  concerning  the  liquor  Alkehest,  the  Mercury  of 
Philosophers,  and  other  curiosities  worthy  the  perusal.  Written 
by  Eir.  Philaletha,  Anonymus,  J.  B.  Van-Helmont,  Dr.  Fr. 
Antonie,  Bernhard  Earl  of  Trevisan,  Sir  Geo.  Bipley,  Rog. 
Bacon,  Geo.  Starkie,  Sir  Hugh  Platt,  and  the  Tomb  of  Semira- 
mis.  See  more  in  the  contents.  London,  1684,  8vo. 

In-  the  advertisements  at  the  ends  of  these  tracts  there  are 
upwards  of  a  hundred  English  tracts,  nearly  all  of  the  per:od, 
and  most  of  them  translations.  Alchemy  looks  up  since  the 
chemists  have  found  perfectly  different  substances  composed  of 
the  same  elements  and  proportions.  It  is  true  the  chemists 
cannot  yet  transmute  ;  but  they  may  in  time  :  they  poke  about 
most  assiduously.  It  seems,  then,  that  the  conviction  that 
alchemy  must  be  impossible  was  a  delusion:  but  we  do  not 
mention  it. 

The  astrologers  and  the  alchemists  caught  it  in  company  in 
the  following,  of  which  I  have  an  unreferenced  note. 

Mendacem  et  futilem  hominem  nominare  qui  volunt,  calenda- 
riographum.  dicunt  ;  at  qui  sceleratum  simul  ac  impostorem, 
chimicum. 

Credo  ratem  rentis,  corpus  ne  crede  chimistis  ; 
Est  qusevis  chimica  tutior  aura  fide. 

Among  the  smaller  paradoxes  of  the  day  is  that  of  the  Times 
newspaper,  which  always  spells  it  chymistry  :  but  so,  I  believe, 
do  Johnson,  Walker,  and  others.  The  Arabic  word  is  very  likely 
formed  from  the  Greek  :  but  it  may  be  connected  either  with 
or  with 


Lettre  d'un  gentil-homme  de  province  a  une  dame  de  qualite, 
sur  le  sujet  de  la  Comete.     Paris,  1681,  4to. 

An  opponent  of  astrology,  whom  I  strongly  suspect  to  have 
been  one  of  the  members  of  the  Academy  of  Sciences  under  the 
name  of  a  country  gentleman,  writes  very  good  sense  on  the 
tremors  excited  by  comets. 


76  A  BUDGET  OF  PARADOXES. 


The  Petitioning- Comet :  or,  a  brief  Chronology  of  all  the  famous 
Comets  and  their  events,  that  have  happened  from  the  birth  of 
Christ  to  this  very  day.  Together  with  a  modest  enquiry  into 
this  present  comet,  London,  1681,  4to. 

A  satirical  tract  against  cometic  prophecy  : — 

'  This  present  comet  (it's  true)  is  of  a  menacing  aspect,  but  if  the 
neiv parliament  (for  whose  convention  so  many  good  men  pray)  continue 
long  to  sit,  I  fear  not  but  the  star  will  lose  its  virulence  and  malignancy, 
or  at  least  its  portent  be  averted  from  this  our  nation ;  which  being 
the  humble  request  to  God  of  all  good  men,  makes  me  thus  entitle  it, 
a  Petitioning-Comet. 

The  following  anecdote  is  new  to  me : — 

Queen  Elizabeth  (1558)  being  then  at  Richmond,  and  being 
disswaded  from  looking  on  a  comet  which  did  then  appear,  made 
answer,  jacta  est  alea,  the  dice  are  thrown ;  thereby  intimating  that 
the  pre-order'd  providence  of  God  was  above  the  influence  of  any  star 
or  comet. 

The  argument  was  worth  nothing :  for  the  comet  might  have 
been  on  the  dice  with  the  event ;  the  astrologers  said  no  more, 
at  least  the  more  rational  ones,  who  were  about  half  of  the 
whole. 

An  astrological  and  theological  discourse  upon  this  present 
great  conjunction  (the  like  whereof  hath  not  (likely)  been  in 
some  ages)  ushered  in  by  a  great  comet.  London,  1682,  4to. 
By  C.  ST. 

The  author  foretells  the  approaching  '  sabbatical  jubilee,'  but 
will  not  fix  the  date :  he  recounts  the  failures  of  his  predeces- 
sors. 

A  judgment  of  the  comet  which  became  first  generally  visible 
to  us  in  Dublin,  December  13,  about  15  minutes  before  5  in  the 
evening,  A.D.  1680.  By  a  person  of  quah'ty.  Dublin,  1682, 
4to. 

The  author  argues  against  cometic  astrology  with  great  ability. 

A  prophecy  on  the  conjunction  of  Saturn  and  Jupiter  in  this 
present  year  1682.  With  some  prophetical  predictions  of  what 
is  likely  to  ensue  therefrom  in  the  year  1684.  By  John  Case, 
Student  in  physic  and  astrology.  London,  1682,  4to. 

According  to  this  writer,  great  conjunctions  of  Jupiter  and 
Saturn  occur  'in  the  fiery  trigon,'  about  once  in  800  years.  Of 


MARCELIS.      MATHEMATICAL   THEOLOGY.  77 

these  there  are  to  be  seven :  six  happened  in  the  several  times 
of  Enoch,  Noah,  Moses,  Solomon,  Christ,  Charlemagne.  The 
seventh,  which  is  to  happen  at  '  the  lamb's  marriage  with  the 
bride,'  seems  to  be  that  of  1682  ;  but  this  is  only  vaguely  hinted. 

De  Quadrature  van  de  Circkel.    By  Jacob  Marcelis.     Amsterdam, 

1698,  4to. 
Ampliatie  en  demonstratie  wegens  de  Quadrature  .  .  .  By  Jacob 

Marcelis.     Amsterdam,  1699,  4to. 
Eenvoudig   vertoog   briev-wys    geschrevem   am    J.    Marcelis  .  . 

Amsterdam,  1702,  4to. 
De  sleutel   en   openinge    van   de  quadrature.    .    .    .   Amsterdam, 

1704,  4to. 

Who  shall  contradict  Jacob  Marcelis  ?     He  says  the  circum- 
ference contains  the  diameter  exactly  times 

0100844908737754167989428218489J4 
6997183037540819440035239271702 

But  he  does  not  come  very  near,  as  the  young  arithmetician  will 
rind. 

Theologiffi  Christianas  Principia  Mathematica.     Auctore  Johanne 
Craig.     London,  1699,  4to. 

This  is  a  celebrated  speculation,  and  has  been  reprinted  abroad, 
and  seriously  answered.  Craig  is  known  in  the  early  history  of 
fluxions,  and  was  a  good  mathematician.  He  professed  to  calcu- 
late, on  the  hypothesis  that  the  suspicions  against  historical 
evidence  increase  with  the  square  of  the  time,  how  long  it  will 
take  the  evidence  of  Christianity  to  die  out.  He  finds,  by 
formulae,  that  had  it  been  oral  only,  it  would  have  gone  out 
A.D.  800 ;  but,  by  aid  of  the  written  evidence,  it  will  last  till 
A.D.  3150.  At  this  period  he  places  the  second  coming,  which  is 
deferred  until  the  extinction  of  evidence,  on  the  authority  of  the 
question  '  When  the  Son  of  Man  cometh,  shall  he  find  faith  on 
the  earth  ?  '  It  is  a  pity  that  Craig's  theory  was  not  adopted  :  it 
would  have  spared  a  hundred  treatises  on  the  end  of  the  world, 
founded  on  no  better  knowledge  than  his,  and  many  of  them 
falsified  by  the  event.  The  most  recent  (October,  1863)  is  a 
tract  in  proof  of  Louis  Napoleon  being  Antichrist,  the  Beast,  the 
eighth  Head,  &c.;  and  the  present  dispensation  is  to  close  soon 
after  1864. 

In  order  rightly  to  judge  Craig,  who  added  speculations  on  the 
variations  of  pleasure  and  pain  treated  as  functions  of  time,  it  is 


78  A  BUDGET   OF  PAEADOXES. 

necessary  to  remember  that  in  Newton's  day  the  idea  of  force,  as  a 
quantity  to  be  measured,  and  as  following  a  law  of  variation,  was 
very  new :  so  likewise  was  that  of  probability,  or  belief,  as  an  object 
of  measurement.  The  success  of  the  '  Principia '  of  Newton  put  it 
into  many  heads  to  speculate  about  applying  notions  of  quantity 
to  other  things  not  then  brought  under  measurement.  Craig 
imitated  Newton's  title,  and  evidently  thought  he  was  making 
a  step  in  advance :  but  it  is  not  every  one  who  can  plough  with 
Samson's  heifer. 

It  is  likely  enough  that  Craig  took  a  hint,  directly  or  in- 
directly, from  Mahometan  writers,  who  make  a  reply  to  the 
argument  that  the  Koran  has  not  the  evidence  derived  from 
miracles.  They  say  that,  as  evidence  of  Christian  miracles  is 
daily  becoming  weaker,  a  time  must  at  last  arrive  when  it  will 
fail  of  affording  assurance  that  they  were  miracles  at  all : 
whence  would  arise  the  necessity  of  another  prophet  and  other 
miracles.  Lee,  the  Cambridge  orientalist,  from  whom  the  above 
words  are  taken,  almost  certainly  never  heard  of  Craig  or  his 
theory. 

Copernicans  of  all  sorts  convicted  ...  to  which  is  added  a  Treatise 
of  the  Magnet.  By  the  Hon.  Bdw.  Howard,  of  Berks.  London, 
1705,  8vo. 

Not  all  the  blood  of  all  the  Howards  will  gain  respect  for  a 
writer  who  maintains  that  eclipses  admit  no  possible  explanation 
under  the  Copernican  hypothesis,  and  who  asks  how  a  man  can 
'  go  200  yards  to  any  place  if  the  moving  superficies  of  the  earth 
does  carry  it  from  him  ? '  Horace  Walpole,  at  the  beginning  of 
his  '  Eoyal  and  Noble  Authors,'  has  mottoed  his  book  with  the 
Cardinal's  address  to  Ariosto,  'Dove  diavolo,  Messer  Ludovico, 
avete  pigliato  tante  coglionerie  ? '  Walter  Scott  says  you  could 
hardly  pick  out,  on  any  principle  of  selection — except  badness 
itself,  he  means  of  course — the  same  number  of  plebeian  authors 
whose  works  are  so  bad.  But  his  implied  satire  on  aristocratic 
writing  forgets  two  points.  First,  during  a  large  period  of  our 
history,  when  persons  of  rank  condescended  to  write,  they  veiled 
themselves  under  'a  person  of  honour,'  '  a  person  of  quality,'  and 
the  like,  when  not  wholly  undescribed.  Not  one  of  these  has 
Walpole  got ;  he  omits,  for  instance,  Lord  Brounker's  translation 
of  Descartes  on  Music.  Secondly,  Walpole  only  takes  the  heads 
of  houses  :  this  cuts  both  ways  ;  he  equally  eliminates  the  Hon. 
Robert  Boyle  and  the  precious  Edward  Howard.  This  last  writer 
is  hardly  out  of  the  time  in  which  aristocracy  suppressed  its 


WHISTON,  DITTOS,  AND   SWIFT.  79 

names ;  the  avowal  was  then  usually  meant  to  make  the  author's 
greatness  useful  to  the  book.  In  our  day,  literary  peers  and 
honourables  are  very  favourably  known,  and  contain  an  eminent 
class.  They  rough  it  like  others,  and  if  such  a  specimen  as  Edw. 
Howard  were  now  to  appear,  he  would  be  greeted  with 

Hereditary  noodle  !  knowest  thou  not, 

Who  would  be  wise,  himself  must  make  him  so  ? 

A  new  and  easy  method  to  find  the  longitude  at  land  or  sea. 
London,  1710,  4to. 

This  tract  is  a  little  earlier  than  the  great  epoch  of  such  publi- 
cations (1714),  and  professes  to  find  the  longitude  by  the  observed 
altitudes  of  the  moon  and  two  stars. 

A  new  method  for  discovering  the  longitude  both  at  sea  and 
land,  humbly  proposed  to  the  consideration  of  the  public.  By 
Wm.  Whiston  and  Humphry  Ditton.  London,  1714,  8vo. 

This  is  the  celebrated  tract,  written  by  the  two  Arian  heretics. 
Swift,  whose  orthodoxy  was  as  undoubted  as  his  meekness,  wrote 
upon  it  the  epigram  if,  indeed,  that  be  epigram  of  which  the 
point  is  pious  wish — which  has  been  so  often  recited  for  the 
purity  of  its  style,  a  purity  which  transcends  modern  printing. 
Perhaps  some  readers  may  think  that  Swift  cared  little  for  Whiston 
and  Ditton,  except  as  a  chance  hearing  of  their  plan  pointed  them 
out  as  good  marks.  But  it  was  not  so  :  the  clique  had  their  eye 
on  the  guilty  pair  before  the  publication  of  the  tract.  The  pre- 
face is  dated  July  7 ;  and  ten  days  afterwards  Arbuthnot  writes 
as  follows  to  Swift : — 

Whiston  has  at  last  published  his  project  of  the  longitude  ;  the  most 
ridiculous  thing  that  ever  was  thought  on.  But  a  pox  on  him  !  lie  has 
spoiled  one  of  my  papers  of  Scriblerus,  which  was  a  proposition  for  the 
longitude  not  very  unlike  his,  to  this  purpose  ;  that  since  there  was  no 
pole  for  east  and  west,  that  all  the  princes  of  Europe  should  join  and 
build  two  prodigious  poles,  upon  high  mountains,  with  a  vast  lighthouse 
to  serve  for  a  polestar.  I  was  thinking  of  a  calculation  of  the  time, 
charges,  and  dimensions.  Now  you  must  understand  his  project  is  by 
lighthouses,  and  explosion  of  bombs  at  a  certain  hour. 

The  plan  was  certainly  impracticable  ;  but  Whiston  and  Ditton 
might  have  retorted  that  they  were  nearer  to  the  longitude  than 
their  satirist  to  the  kingdom  of  heaven,  or  even  to  a  bishopric. 
Arbuthnot,  I  think,  here  and  elsewhere,  reveals  himself  as  the 
calculator  who  kept  Swift  right  in  his  proportions  in  the  matter 


80  A   BUDGET   OF  PARADOXES. 

of  the  Lilliputians,  Brobdingnagians,  &c.  Swift  was  very  ignorant 
about  things  connected  with  number.  He  writes  to  Stella  that 
he  has  discovered  that  leap-year  comes  every  four  years,  and  that 
all  his  life  he  had  thought  it  came  every  three  years.  Did  he 
begin  with  the  mistake  of  Caesar's  priests  ?  Whether  or  no,  when 
I  find  the  person  who  did  not  understand  leap-year  inventing 
satellites  of  Mars  in  correct  accordance  with  Kepler's  third  law, 
I  feel  sure  he  must  have  had  help. 


An  essay  concerning  the  late  apparition  in  the  heavens  on  the 
6th  of  March.  Proving  by  mathematical,  logical,  and  moral 
arguments,  that  it  cou'd  not  have  been  produced  meerly  by  the 
ordinary  course  of  nature,  but  must  of  necessity  be  a  prodigy. 
Humbly  offered  to  the  consideration  of  the  Royal  Society. 
London,  1716,  8vo. 

The  prodigy,  as  described,  was  what  we  should  call  a  very 
decided  and  unusual  aurora  borealis.  The  inference  was,  that 
men's  sins  were  bringing  on  the  end  of  the  world.  The  author 
thinks  that  if  one  of  the  old  '  threatening  prophets '  were  then 
alive,  he  would  give  '  something  like  the  following.'  I  quote  a 
few  sentences  of  the  notion  which  the  author  had  of  the  way  in 
which  Ezekiel,  for  instance,  would  have  addressed  his  Maker  in 
the  reign  of  George  the  First : — 

Begin  !  Begin  !  0  Sovereign,  for  once,  with  an  effectual  clap  of 
thunder.  ...  0  Deity  !  either  thunder  to  us  no  more,  or  when  you 
thunder,  do  it  home,  and  strike  with  vengeance  to  the  mark.  .  .  .  'Tis 
not  enough  to  raise  a  storm,  unless  you  follow  it  with  a  blow,  and  the 
thunder  without  the  bolt,  signifies  just  nothing  at  all.  .  .  .  Are  then 
your  lightnings  of  so  short  a  sight,  that  they  don't  know  how  to  hit, 
unless  a  mountain  stands  like  a  barrier  in  their  way  ?  Or  perhaps  so 
many  eyes  open  in  the  firmament  make  you  lose  your  aim  when  you 
shoot  the  arrow  ?  Is  it  this  ?  No  !  but,  my  dear  Lord,  it  is  your 
custom  never  to  take  hold  of  your  arms  till  you  have  first  bound  round 
your  majestic  countenance  with  gathered  mists  and  clouds. 

The  principles  of  the  Philosophy  of  the  Expansive  and  Con- 
tractive Forces.  ...  By  Robert  Greene,  M.A.,  Fellow  of  Clare 
Hall.  Cambridge,  1727,  folio. 

Sanderson  writes  to  Jones :  'The  gentleman  has  been  reputed 
mad  for  these  two  years  last  past,  but  never  gave  the  world  such 
ample  testimony  of  it  before.'  This  was  said  of  a  former  work  of 
Greene's,  on  solid  geometry,  published  in  1712,  in  which  he  gives 


NEWTON'S   APPLE.  81 

a  quadrature.  He  gives  the  same  or  another,  I  do  not  know 
which,  in  the  present  work,  in  which  the  circle  is  3^-  diameters. 
This  volume  is  of  981  good  folio  pages,  and  treats  of  all  thino-s, 
mental  and  material.  The  author  is  not  at  all  mad,  only  wrong 
on  many  points.  It  is  the  weakness  of  the  orthodox  follower  of 
any  received  system  to  impute  insanity  to  the  solitary  dissentient  : 
which  is  voted  (in  due  time)  a  very  wrong  opinion  about  Coper- 
nicus, Columbus,  or  Galileo,  but  quite  right  about  Robert  Greene. 
If  misconceptions,  acted  on  by  too  much  self-opinion,  b$  sufficient 
evidence  of  madness,  it  would  be  a  curious  inquiry  what  is  the 
least  per-centage  of  the  reigning  school  which  has  been  insane  at 
any  one  time.  Greene  is  one  of  the  sources  for  Newton  being  led 
to  think  of  gravitation  by  the  fall  of  an  apple  :  his  authorit"7  is 
the  gossip  of  Martin  Folkes.  Probably  Folkes  had  it  from 
Newton's  niece,  Mrs.  Conduitt,  whom  Voltaire  acknowledges  as 
//'">•  authority.  It  is  in  the  draft  found  among  Conduitt's  papers 
of  memoranda  to  be  sent  to  Fontenelle.  But  Fontenelle,  though 
a  great  retailer  of  anecdote,  does  not  mention  it  in  his  eloge  of 
Newton  ;  whence  it  may  be  suspected  that  it  was  left  out  in  the 
copy  forwarded  to  France.  D'Israeli  has  got  an  improvement  on 
the  story  :  the  apple  *  struck  him  a  smart  blow  on  the  head  : '  no 
doubt  taking  him  just  on  the  organ  of  causality.  He  was '  surprised 
at  the  force  of  the  stroke '  from  so  small  an  apple  :  but  then  the 
apple  had  a  mission  ;  Homer  would  have  said  it  was  Minerva  in 
the  form  of  an  apple.  '  This  led  him  to  consider  the  accelerating 
motion  of  falling  bodies,'  which  Galileo  had  settled  long  before  : 
'  from  whence  he  deduced  the  principle  of  gravity,'  which  many 
had  considered  before  him,  but  no  one  had  deduced  anything  from 
it.  I  cannot  imagine  whence  D'Israeli  got  the  rap  on  the  head, 
I  mean  got  it  for  Newton  :  this  is  very  unlike  his  usual  accounts 
of  things.  The  story  is  pleasant  and  possible  :  its  only  defect  is 
that  various  writings,  well  known  to  Newton,  a  very  learned 
mathematician,  had  given  more  suggestion  than  a  whole  sack  of 
apples  could  have  done,  if  they  had  tumbled  on  that  mighty  head 
all  at  once.  And  Pemberton,  speaking  from  Newton  himself, 
says  nothing  more  than  that  the  idea  of  the  moon  being  retained 
by  the  same  force  which  causes  the  fall  of  bodies  struck  him  for 
the  first  time  while  meditating  in  a  garden.  One  particular  tree 
at.  Woolsthorpe  has  been  selected  as  the  gallows  of  the  apple- 
shaped  goddess:  it  died  in  1820,  and  Mr.  Tumor  kept  the  wood  ; 
but  Sir  D.  Brewster  brought  away  a  bit  of  root  in  1814,  and  must 
have  had  it  on  his  conscience  for  43  years  that  he  may  have  killed 
the  tree.  Kepler's  suggestion  of  gravitation  with  the  inverse 

G 


82  A  BUDGET   QF   PARADOXES. 

distance,  and  Bouillaud's  proposed  substitution  of  the  inverse 
square  of  the  distance,  are  things  which  Newton  knew  better  than 
his  modern  readers.  I  discovered  two  anagrams  on  his  name, 
which  are  quite  conclusive  :  the  notion  of  gravitation  was  not 
new ;  but  Newton  vuent  on.  Some  wandering  spirit,  probably, 
whose  business  it  was  to  resent  any  liberty  taken  with  Newton's 
name,  put  into  the  head  of  a  friend  of  mine  eighty-one  anagrams 
on  my  own  pair,  some  of  which  hit  harder  than  any  apple. 

This  friend,  whom  I  must  not  name,  has  since  made  it  up  to 
about  800  anagrams  on  my  name,  of  which  I  have  seen  about 
650.  Two  of  them  I  have  joined  in  the  title-page  :  the  reader 
may  find  the  sense.  A  few  of  the  others  are  personal  remarks. 

Great  gun  !  do  us  a  sum  ! 
is  a  sneer  at  my  pursuits :  but, 

Go  !  great  sum  !  fau  du 

is  more  dignified. 

Sunt  agro  !  gaudemus, 

is  happy  as  applied  to  one  of  whom  it  may  be  said  : 

Ne'er  out  of  town  ;  'tis  such  a  horrid  life  : 
But  duly  sends  his  family  and  wife. 

Adsum,  nugator,  suge ! 

is  addressed  to  a  student  who  continues  talking  after  the  lecture 
has  commenced  :  oh  !  the  rascal ! 

Graduatus  sum !  nego 
applies  to  one  who  declined  to  subscribe  for  an  M.A.  degree. 

Usage  mounts  guard 
symbolises  a  person  of  very  fixed  habits. 

Gus  !     Gus  !  a  mature  don  ! 

August  man  !  sure,  god  ! 
And  Gus  must  argue,  0  ! 

Snug  as  mud  to  argue, 
Must  argue  on  gauds. 

A  mad  rogue  stung  us. 
Gag  a  numerous  stud. 

Go  !  turn  us  !  damage  us  ! 
Tug  us  !     O  drag  us  !     Amen. 

Grudge  us  !  moan  at  us  ! 
Daunt  us  !  gag  us  more  ! 

TJog-ear  us,  man  !  gut  us  ! 
D —  us  !  a  ro^ue  tuers  ! 


TREATISE   ASCRIBED   TO   NEWTON.  83 

are  addressed  to  me  by  the  circle-squarers  ;  and, 
O  !  Gus  !  tug  a  mean  surd  ! 

is  smart  upon  my  preference  of  an  incommensurable  value  of  TT 
to  3^,  or  some  such  simple  substitute.     While, 
Gus  !  Gus  !  at  'em  a'  round  ! 

ought  to  be  the  backing  of  the  scientific  world  to  the  author  of 
the  c  Budget  of  Paradoxes.' 

The  whole  collection  commenced  existence  in  the  head  of  a 
powerful  mathematician  during  some  sleepless  nights.  Seeing 
how  large  a  number  was  practicable,  he  amused  himself  by  in- 
venting a  digested  plan  of  finding  more. 

Is  there  any  one  whose  name  cannot  be  twisted  into  either 
praise  or  satire  ?  I  have  had  given  to  me, 

Thomas  Babington  Macaulay 
Mouths  big  :  a  Cantab  anomaly. 

A   treatise  of  the  system  of  the  world.     By  Sir  Isaac  Newton. 
Translated  into  English.     London,  1728,  8vo. 

I  think  I  have  a  right  to  one  little  paradox  of  my  own :  I 
greatly  doubt  that  Newton  wrote  this  book.  Castiglione,  in  his 
'Newtoni  Opuscula,'  gives  it  in  the  Latin  which  appeared  in  1731, 
not  for  the  first  time  ;  he  says  Angli  omnes  Newtono  trihuunt.  It 
appeared  just  after  Newton's  death,  without  the  name  of  any 
editor,  or  any  allusion  to  Newton's  recent  departure,  purporting 
to  be  that  popular  treatise  which  Newton,  at  the  beginning  of 
the  third  book  of  the  *  Principia,'  says  he  wrote,  intending  it  to 
be  the  third  book.  It  is  very  possible  that  some  observant  turn- 
penny might  construct  such  a  treatise  as  this  from  the  third  book, 
that  it  might  be  ready  for  publication  the  moment  Newton  could 
not  disown  it.  It  has  been  treated  with  singular  silence :  the 
name  of  the  editor  has  never  been  given.  Riband  mentions  it 
without  a  word  :  I  cannot  find  it  in  Brewster's  Newton,  nor  in  the 
'  Biographia  Britannica.'  There  is  no  copy  in  the  Catalogue  of 
the  Royal  Society's  Library,  either  in  English  or  Latin,  except  in 
Castiglione.  I  am  open  to  correction  ;  but  I  think  nothing  from 
Newton's  acknowledged  works  will  prove — as  laid  down  in  the 
suspected  work — that  he  took  Numa's  temple  of  Vesta,  with  a 
central  fire,  to  be  intended  to  symbolise  the  sun  as  the  centre  of 
our  system,  in  the  Copernican  sense. 

Mr.Edleston  gives  an  account  of  the  lectures  '  de  motu  corporum,* 
and  gives  the  corresponding  pages  of  the  Latin  '  De 

o  2 


84  A  BUDGET   OF   PAEADOXES. 

Mundi'  of  1731.  But  no  one  mentions  the  English  of  1728. 
This  English  seems  to  agree  with  the  Latin ;  but  there  is  a  mystery 
about  it.  The  preface  says,  '  That  this  work  as  here  published  is 
genuine  will  so  clearly  appear  by  the  intrinsic  marks  it  bears,  that 
it  will  be  but  losing  words  and  the  reader's  time  to  take  pains  in 
giving  him  any  other  satisfaction.'  Surely  fewer  words  would 
have  been  lost  if  the  prefator  had  said  at  once  that  the  work  was 
from  the  manuscript  preserved  at  Cambridge.  Perhaps  it  was  a 
mangled  copy  clandestinely  taken  and  interpolated. 

Lord  Bacon  not  the  author  of  'The  Christian  Paradoxes,'  being 
a  reprint  of  '  Memorials  of  Godliness  and  Christianity,'  by 
Herbert  Palmer,  B.D.  With  Introduction,  Memoir,  and  Notes, 
by  the  Rev.  Alexander  B.  Grosart,  Kenross.  (Private  circulation, 
1864). 

I  insert  the  above  in  this  place  on  account  of  a  slight  con- 
nexion with  the  last.  Bacon's  Paradoxes, — so  attributed — were 
first  published  as  his  in  some  asserted  '  Kemains,'  1648.  They 
were  admitted  into  his  works  in  1730,  and  remain  there  to  this 
day.  The  title  is  'The  Character  of  a  believing  Christian,  set 
forth  in  paradoxes  and  seeming  contradictions.'  The  following  is 
a  specimen : — 

He  believes  three  to  be  one  and  one  to  be  three  ;  a  father  not  to  be 
older  than  his  son ;  a  son  to  be  equal  with  his  father  ;  and  one  pro- 
ceeding from  both  to  be  equal  with  both  :  he  believes  three  persons  in 

one  nature,  and  two  natures  in  one  person He  believes  the  God 

of  all  grace  to  have  been  angry  with  one  that  never  offended  Him  ;  and 
that  God  that  hates  sin  to  be  reconciled  to  himself  though  sinning  con- 
tinually, and  never  making  or  being  able  to  make  Him  any  satisfaction. 
He  believes  a  most  just  God  to  have  punished  a  most  just  person,  and 
to  have  justified  himself,  though  a  most  ungodly  sinner.  He  believes 
himself  freely  pardoned,  and  yet  a  sufficient  satisfaction  was  made  for 
Mm. 

Who  can  doubt  that  if  Bacon  had  written  this,  it  must  have 
been  wrong?  Many  writers,  especially  on  the  Continent,  have 
taken  him  as  sneering  at  (Athanasian)  Christianity  right  and  left. 
Many  Englishmen  have  taken  him  to  be  quite  in  earnest,  and  to 
have  produced  a  body  of  edifying  doctrine.  More  than  a  century 
ago  the  Paradoxes  were  published  as  a  penny  tract ;  and,  again,  at 
the  same  price,  in  the  'Penny  Sunday  Eeader,'  vol.  vi.  No.  148,  a 
few  passages  were  omitted,  as  too  strong.  But  all  did  not  agree  : 
in  my  copy  of  Peter  Shaw's  edition  (vol.  ii.  p.  283)  the  Paradoxes 
have  been  cut  out  by  the  binder,  who  has  left  the  backs  of  the 
leaves.  I  never  had  the  curiosity  to  see  whether  other  copies  of 


BACON'S  PARADOXES.      SOCINIANS  AND  UNITARIANS.  85 

the  edition  have  been  served  in  the  same  way.  The  Keligious 
Tract  Society  republished  them  recently  in  '  Selections  from  the 
Writings  of  Lord  Bacon,'  (no  date;  bad  plan;  about  1863,  I 
suppose).  No  omissions  were  made,  so  far  as  I  find. 

I  never  believed  that  Bacon  wrote  this  paper  ;  it  has  neither  his 
sparkle  nor  his  idiom.  I  stated  my  doubts  even  before  I  heard 
that  Mr.  Spedding,  one  of  Bacon's  editors,  was  of  the  same  mind. 
(Athenceum,  July  16,  1864).  I  was  little  moved  by  the  wide  con- 
sent of  orthodox  men :  for  I  knew  how  Bacon,  Milton,  Newton, 
Locke,  &c.,  were  always  claimed  as  orthodox  until  almost  the 
present  day.  Of  this  there  is  a  remarkable  instance. 

Among  the  books  which  in  my  younger  day  were  in  some 
orthodox  publication  lists — I  think  in  the  list  of  the  Christian 
Knowledge  Society,  but  I  am  not  sure— was  Locke's  '  Eeason- 
ableness  of  Christianity.'  It  seems  to  have  come  down  from  the 
eighteenth  century,  when  the  battle  was  belief  in  Christ  against 
unbelief,  simplicite)^  as  the  logicians  say.  Now,  if  ever  there 
were  a  Socinian1  book  in  the  world,  it  is  this  work  of  Locke. 
'  These  two,'  says  Locke,  '  faith  and  repentance,  i.e.  believing 
Jesus  to  be  the  Messiah,  and  a  good  life,  are  the  indispensable 
conditions  of  the  new  covenant,  to  be  performed  by  all  those  who 
would  obtain  eternal  life.'  AIL  the  book  is  amplification  of  this 
doctrine.  Locke,  in  this  and  many  other  things,  followed  Hobbes, 
whose  doctrine,  in  the  Leviathan,  is  fidem,  quanta  ad  salutem 
necessaria  est,  contineri  in  hoc  articulo,  Jesus  est  Christus.  For 
this  Hobbes  was  called  an  atheist,  which  many  still  believe  him 
to  have  been :  some  of  his  contemporaries  called  him,  rightly, 

1  I  use  the  word  Socinian  because  it  was  so  much  used  in  Locke's  time ;  it  is  used 
in  our  own  day  by  the  small  fry,  the  unlearned  clergy  and  their  immediate  followers, 
as  a  term  of  reproach  for  all  Unitarians.  I  suspect  they  have  a  kind  of  liking  for  the 
word ;  it  sounds  like  so  sinful.  The  learned  clergy  and  the  higher  laity  know  better : 
they  know  that  the  bulk  of  the  modern  Unitarians  go  farther  than  Socinus,  and  are 
not  correctly  named  as  his  followers.  The  Unitarians  themselves  neither  desire  nor 
deserve  a  name  which  puts  them  one  point  nearer  to  orthodoxy  than  they  put 
themselves.  That  point  is  the  doctrine  that  direct  prayer  to  Jesus  Christ  is  lawful 
and  desirable  :  this  Socinus  held,  and  the  modern  Unitarians  do  not  hold.  Socinus, 
in  treating  the  subject  in  his  own  Insdtutio,  an  imperfect  catechism  which  he  left,  lays 
much  more  stress  on  John  xiv.  13  than  on  XT.  16  and  xvi.  23.  He  is  not  disinclined  to 
think  that  Patrem  should  be  in  the  first  citation,  where  some  put  it  ;  but  he  says 
that  to  ask  the  Father  in  the  name  of  the  Son  is  nothing  but  praying  to  the  Son  in 
prayer  to  the  Father.  He  labours  the  point  with  obvious  wish  to  secure  a  conclusive 
sanction.  In  the  Racovian  Catechism,  of  which  Faustus  Socinus  probably  drew  the 
first  sketch,  a  clearer  light  is  arrived  at.  The  translation  says  :  '  But  wherein  con- 
sists  the  divine  honour  due  to  Christ?  In  adoration  likewise  and  invocation.  For 
we  ought  at  all  times  to  adore  Christ,  and  may  in  our  necessities  address  our  pray*  ia 
to  him  as  often  as  we  please;  and  there  are  many  reasons  to  induce  us  to  do  this 
freely.'  There  are  some  who  like  accuracy,  even  in  aspersion. 


86  A  BUDGET   OF  PARADOXES. 

a  Socinian.  Locke  was  known  for  a  Socinian  as  soon  as  his  work 
appeared  :  Dr.  John  Edwards,  his  assailant,  says  he  is  '  Socin- 
ianized  all  over.'  Locke,  in  his  reply,  says  'there  is  not  one 
word  of  Socinianism  in  it : '  and  he  was  right :  the  positive 
Socinian  doctrine  has  not  one  word  of  Socinianism  in  it;  So- 
cinianism consists  in  omissions.  Locke  and  Hobbes  did  not  dare 
deny  the  Trinity :  for  such  a  thing  Hobbes  might  have  been 
roasted,  and  Locke  might  have  been  strangled.  Accordingly,  the 
well  known  way  of  teaching  Unitarian  doctrine  was  the  collection 
of  the  asserted  essentials  of  Christianity,  without  naming  the 
Trinity,  &c.  This  is  the  plan  Newton  followed,  in  the  papers  which 
have  at  last  been  published. 

So  I,  for  one,  thought  little  about  the  general  tendency  of 
orthodox  writers  to  claim  Bacon  by  means  of  the  Paradoxes.  I 
knew  that,  in  his  '  Confession  of  Faith  '  he  is  a  Trinitarian  of  a 
heterodox  stamp.  His  second  Person  takes  human  nature  before 
he  took  flesh,  not  for  redemption,  but  as  a  condition  precedent  of 
creation.  '  God  is  so  holy,  pure,  and  jealous,  that  it  is  impossible 
for  him  to  be  pleased  in  any  creature,  though  the  work  of  his 

own    hands [Genesis    i.    10,    12,    18,    21,  25,    31,    freely 

rendered].  But — purposing  to  become  a  Creator,  and  to  commu- 
nicate to  his  creatures,  he  ordained  in  his  eternal  counsel  that 
one  person  of  the  Godhead  should  be  united  to  one  nature,  and 
to  one  particular  of  his  creatures  ;  that  so,  in  the  person  of 
the  Mediator,  the  true  ladder  might  be  fixed,  whereby  God 
might  descend  to  his  creatures  and  his  creatures  might  ascend 
to  God ' 

This  is  republished  by  the  Eeligious  Tract  Society,  and  seems 
to  suit  their  theology,  for  they  confess  to  having  omitted  some 
things  of  which  they  disapprove. 

In  1864,  Mr.  Grosart  published  his  discovery  that  the  Paradoxes 
are  by  Herbert  Palmer ;  that  they  were  first  published  surrep- 
titiously, and  immediately  afterwards  by  himself,  both  in  1645 ; 
that  the  *  Eemains '  of  Bacon  did  not  appear  until  1 648 ;  that 
from  1645  to  1708,  thirteen  editions  of  the  'Memorials'  were 
published,  all  containing  the  Paradoxes.  In  spite  of  this,  the 
Paradoxes  were  introduced  into  Bacon's  works  in  1730,  where  they 
have  remained. 

Herbert  Palmer  was  of  good  descent,  and  educated  as  a  Puri- 
tan. He  was  an  accomplished  man,  one  of  the  few  of  his  day  who 
could  speak  French  as  well  as  English.  He  went  into  the  Church, 
and  was  beneficed  by  Laud,  in  spite  of  his  puritanism  ;  he  sat  in 
the  Assembly  of  Divines,  and  was  finally  President  of  Queens' 


CIRCLE  SQUARERS.      WHISTON   ON  THE  LONGITUDE.  87 

College,  Cambridge,  in  which  post  he  died,  August  13, 1647,  in  the 
46th  year  of  his  age. 

Mr.  Grosart  says,  speaking  of  Bacon's  '  Eemains,'  '  All  who  have 
had  occasion  to  examine  our  early  literature  are  aware  that  it  was 
a  common  trick  to  issue  imperfect,  false,  and  unauthorised  writings 
under  any  recently  deceased  .name  that  might  be  expected  to  take. 
The  Puritans,  down  to  John  Bunyan,  were  perpetually  expos- 
tulating and  protesting  against  such  procedure.'  I  have  met  with 
instances  of  all  this ;  but  I  did  not  know  that  there  was  so  much 
of  it :  a  good  collection  would  be  very  useful.  The  work  of  1728, 
attributed  to  Newton,  is  likely  enough  to  be  one  of  the  class. 

Demonstration  de  1'immobilitez  de  la  Terre.  .  .  .  Par  M.  de  la 
Jonehere,  Ingenieur  Fran9ais.  Londres,  1728,  8vo. 

A  synopsis  which  is  of  a  line  of  argument  belonging  to  the 
beginning  of  the  preceding  century. 

The  Circle  squared;  together  with  the  Ellipsis  and  several  re- 
flections on  it.  The  finding  two  geometrical  mean  proportionals, 

or  doubling  the  cube  geometrically.     By  Richard  Locke 

London,  no  date,  probably  about  1730,  8vo. 

According  to  Mr.  Locke,  the  circumference  is  three  diameters, 
three-fourths  the  difference  of  the  diameter  and  the  side  of  the 
inscribed  equilateral  triangle,  and  three- fourths  the  difference 
between  seven-eighths  of  the  diameter  and  the  side  of  the  same 
triangle.  This  gives,  he  says,  3-18897.  There  is  an  addition  to 
this  tract,  being  an  appendix  to  a  book  on  the  longitude. 

The  Circle  squar'd.  By  Thos.  Baxter,  Crathorn,  Cleaveland, 
Yorkshire.  London,  1732,  8vo. 

Here  TT  =  3-0625.     No  proof  is  offered. 

The  longitude  discovered  by  the  Eclipses,  Occultations,  and  Con- 
junctions of  Jupiter's  planets.  By  William  Whiston.  London, 
1738. 

This  tract  has,  in  some  copies,  the  celebrated  preface  contain- 
ing the  account  of  Newton's  appearance  before  the  Parliamentary 
Committee  on  the  longitude  question,  in  1714  (Brewster,  ii.  257- 
266).  This  *  historical  preface,'  is  an  insertion,  and  is  dated  April 
28,  1741,  with  four  additional  pages  dated  August  10, 1741.  The 
short  '  preface '  is  by  the  publisher,  John  Whiston,  the  author's 
son. 


88  A  BUDGET   OF  PAEADOXES. 


A- description  and  draught,  of  a  new-invented  machine  for  carrying 
vessels  or  ships  out  of,  or  into  any  harbour,  port,  or  river, 
against  wind  and  ti  le,  or  in  a  calm.  For  which,  His  Majesty 
has  granted  letters  patent,  for  the  sole  benefit  of  the  author,  for 
the  space  of  fourteen  years.  By  Jonathan  Hulls.  London  : 
printed  for  the  author,  1737.  Price  sixpence  (folding  plate  and 
pp.  48,  beginning  from  title). 

(I  ought  to  have  entered  this  tract  in  its  place.  It  is  so  rare 
that  its  existence  was  once  doubted.  It  is  the  earliest  description 
of  steam-power  applied  to  navigation.  The  plate  shows  a  barge, 
with  smoking  funnel,  and  paddles  at  the  stem,  towing  a  ship  of 
war.  The  engine,  as  described,  is  Newcomen's. 

In  1855,  John  Sheepshanks,  so  well  known  as  a  friend  of  Art 
and  a  public  donor,  reprinted  this  tract,  in  fac-simile,  from  his  own 
copy;  twenty-seven  copies  of  the  original  12mo.  size,  and  twelve 
on  old  paper,  small  4to.  I  have  an  original  copy,  wanting  the 
plate,  and  with  '  Price  sixpence '  carefully  erased,  to  the  honour  of 
the  book. 

It  is  not  known  whether  Hulls  actually  constructed  a  boat.  In 
all  probability  his  tract  suggested  to  Symington,  as  Symington  did 
to  Fulton.) 

Le  vrai  systeme  de  physique  generale  de  M.  Isaac  Newton  ex- 
pose et  analyse  en  parallele  avec  celui  de  Descartes.  By 
Louis  Castel  [Jesuit  and  F.R.S.].  Paris,  1743,  4to. 

This  is  an  elaborate  correction  of  Newton's  followers,  and  of 
Newton  himself,  who  it  seems  did  not  give  his  own  views  with 
perfect  fidelity.  Father  Castel,  for  instance,  assures  us  that  New- 
ton placed  the  sun  at  rest  in  the  centre  of  the  system.  Newton  left 
the  sun  to  arrange  that  matter  with  the  planets  and  the  rest  of  the 
universe.  In  this  volume  of  500  pages  there  is  right  and  wrong, 
both  clever. 

A  dissertation  on  the  ^Ether  of  Sir  Isaac  Newton.  By  Bryan 
Robinson,  M.D.  Dublin,  1743,.  8 vo. 

A  mathematical  work,  professing  to  prove  that  the  assumed 
ether  causes  gravitation. 

Mathematical  principles  of  theology,  or  the  existence  of  God 
geometrically  demonstrated.  By  Richard  Jack,  teacher  of 
Mathematics.  London,  1747,  8vo. 

Propositions  arranged  after  the  manner  of  Euclid,  with  beings 
represented  jay  circles  and  squares.  But  these  circles  and  squares 


JOHN  BERNOULLI  AND  DE  FAURE.  89 

are  logical  symbols,  not  geometrical  ones.  I  brought  this  book 
forward  to  the  Eoyal  Commission  on  the  British  Museum  as  an 
instance  of  the  absurdity  of  attempting  a  classed  catalogue  from 
the  titles  of  books.  The  title  of  this  book  sends  it  either  to  theo- 
logy or  geometry :  when,  in  fact,  it  is  a  logical  vagary.  Some  of 
the  houses  which  Jack  built  were  destroyed  by  the  fortune  of  war 
in  1745,  at  Edinburgh  :  who  will  say  the  rebels  did  no  good  what- 
ever ?  I  suspect  that  Jack  copied  the  ideas  of  J.  B.  Morinus, 
'  Quod  Deus  sit,'  Paris,  1636,  4to.,  containing  an  attempt  of  the 
same  kind,  but  not  stultified  with  diagrams. 

Dissertation,  decouverte,  et  demonstrations  de  la  quadrature 
mathematique  du  cercle.  Par  M.  de  Faure,  geometre.  [.<?.  I., 
probably  Geneva]  1747,  8vo. 

Analyse  de  la  Quadrature  du  Cercle.  Par  M.  de  Faure, 
Gentilhomme  Snisse.  Hague,  1749,  4to. 

According  to  this  octavo  geometer  and  quarto  gentleman,  a 
diameter  of  81  gives  a  circumference  of  256.  There  is  an  amusing 
circumstance  about  the  quarto  which  has  been  overlooked,  if 
indeed  the  book  has  ever  been  examined.  John  Bernoulli  (the 
one  of  the  day)  and  Koenig  have  both  given  an  attestation  :  my 
mathematical  readers  may  stare  as  they  please,  such  is  the  fact. 
But,  on  examination,  there  will  be  reason  to  think  the  two  sly 
Swiss  played  their  countryman  the  same  trick  as  the  medical  man 
played  Miss  Pickle,  in  the  novel  of  that  name.  The  lady  only 
wanted  to  get  his  authority  against  sousing  her  little  nephew,  and 
said,  '  Pray,  doctor,  is  it  not  both  dangerous  and  cruel  to  be  the 
means  of  letting  a  poor  tender  infant  perish  by  sousing  it  in  water 
as  cold  as  ice  ? ' — '  Downright  murder,  I  affirm,'  said  the  doctor  ; 
and  certified  accordingly.  De  Faure  had  built  a  tremendous 
scaffolding  of  equations,  quite  out  of  place,  and  feeling  cock-sure 
that  his  solutions,  if  correct,  would  square  the  circle,  applied  to 
Bernoulli  and  Koenig — who  after  his  tract  of  two  years  before, 
must  have  known  what  he  was  at — for  their  approbation  of  the 
solutions.  And  he  got  it,  as  follows,  well  guarded  : — 

Suivant  les  suppositions  posees  dans  ce  Memoire,  il  est  si  evident 
que  t  doit  etre  =  84,  y  =  1,  et  z  =  1,  que  cela  n'a  besoin  ni  de  preuve 
ni  d'autorite  pour  etre  reconnu  par  tout  le  monde. 

a  Basle  le  7e  Mai  1749.  JEAN  BERNOULLI. 

Je  souscris  au  jugement  de  Mr.  Bernoulli,  en  consequence  de  ces 
suppositions. 

a  la  Haye  le  21  Juin  17  I'.'.  S.  KOEXIG. 

On  which  de  Faure  remarks  with  triumph — as  I  have  no  doubt 


90  .         A  BUDGET   OF  PARADOXES. 

it  was  intended  he  should  do — '  il  conste  clairement  par  ma 
presente  Analyse  et  Demonstration,  qu'ils  y  ont  deja  reconnu  et 
approuve  parfaitement  que  la  quadrature  du  cercle  est  mathema- 
tiquement  demontree.'  It  should  seem  that  it  is  easier  to  square 
the  circle  than  to  get  round  a  mathematician. 

An  attempt  to  demonstrate  that  all  the  Phenomena  in  Nature 
may  be  explained  by  two  simple  active  principles,  Attraction 
and  Repulsion,  wherein  the  attractions  of  Cohesion,  Gravity 
and  Magnetism  are  shown  to  be  one  and  the  same.  By  Go  win 
Knight.  London,  1748,  4to. 

Dr.  Knight  was  Mr.  Panizzi's  archetype,  the  first  Principal 
Librarian  of  the  British  Museum.  He  was  celebrated  for  his 
magnetical  experiments.  This  work  was  long  neglected  ;  but  is 
now  recognised  as  of  remarkable  resemblance  to  modern  specula- 
tions. 

An  original  theory  or  Hypothesis  of  the  Universe.  By  Thomas 
Wright  of  Durham.  London,  4to.  1750. 

Wright  is  a  speculator  whose  thoughts  are  now  part  of  our 
current  astronomy.  He  took  that  view — or  most  of  it — of  the 
milky  way  which  afterwards  suggested  itself  to  William  Herschel. 
I  have  given  an  account  of  him  and  his  work  in  the  Philosophi- 
cal Magazine  for  April,  1848. 

Wright  was  mathematical  instrument  maker  to  the  King ;  and 
kept  a  shop  in  Fleet  Street.  Is  the  celebrated  business  of  Trough- 
ton  &  Simms,  also  in  Fleet  Street,  a  lineal  descendant  of  that  of 
Wright  ?  It  is  likely  enough,  more  likely  than  that — as  I  find 
him  reported  to  have  affirmed — Prester  John  was  the  descendant 
of  Solomon  and  the  Queen  of  Sheba.  Having  settled  it  thus,  it 
struck  me  that  I  might  apply  to  Mr.  Simms,  and  he  informs  me 
that  it  is  as  I  thought,  the  line  of  descent  being  Wright,  Cole, 
John  Troughton,  Edward  Troughton,  Troughton  &  Simms. 

The  theology  and  philosophy  in  Cicero's  Somnium  Scipionis 
explained.  Or,  a  brief  attempt  to  demonstrate,  that  the 
Newtonian  system  is  perfectly  agreeable  to  the  notions  of  the 
wisest  ancients  :  and  that  mathematical  principles  are  the  only 
sure  ones.  [By  Bishop  Home,  at  the  age  of  nineteen.] 
London,  1751,  8vo. 

This  tract,  which  was  not  printed  in  the  collected  works,  and  is 
now  excessively  rare,  is  mentioned  in  Notes  and  Queries,  1st  S., 


BISHOP  HORNE  AND   OLD  BEN  MARTIN.  91 

v.  490,  573  ;  2nd  S.,  ix.  15.  The  boyish  satire  on  Newton  is 
amusing.  Speaking  of  old  Benjamin  Martin,  he  goes  on  as 
follows : — 

But  the  most  elegant  account  of  the  matter  [attraction]  is  by  that 
hominiform  animal,  Mr.  Benjamin  Martin,  who  having  attended 
Dr.  Desaguliers'  fine,  raree,  gallanty  shew  for  some  years  [Desa- 
guliers  was  one  of  the  first  who  gave  public  experimental  lectures, 
before  the  saucy  boy  was  born]  in  the  capacity  of  a  turnspit,  has,  it 
seems,  taken  it  into  his  head  to  set  up  for  a  philosopher. 

Thus  is  preserved  the  fact,  unknown  to  his  biographers,  that 
Benj.  Martin  was  an  assistant  to  Desaguliers  in  his  lectures. 
Hutton  says  of  him,  that  '  he  was  well  skilled  in  the  whole  circle 
of  the  mathematical  and  philosophical  sciences,  and  wrote  useful 
books  on  every  one  of  them' :  this  is  quite  true  ;  and  even  at  this 
day  he  is  read  by  twenty  where  Home  is  read  by  one  ;  see  the 
stalls,  passim,.  All  that  I  say  of  him,  indeed  my  knowledge  of 
the  tract,  is  due  to  this  contemptuous  mention  of  a  more  durable 
man  than  himself.  My  assistant  secretary  at  the  AstronomicaJ 
Society,  the  late  Mr.  Epps,  bought  the  copy  at  a  stall  because  his 
eye  was  caught  by  the  notice  of  '  Old  Ben  Martin,'  of  whom  he 
was  a  great  reader.  Old  Ben  could  not  be  a  Fellow  of  the  Royal 
Society,  because  he  kept  a  shop :  even  though  the  shop  sold 
nothing  but  philosophical  instruments.  Thomas  Wright,  similarly 
situated  as  to  shop  and  goods,  never  was  a  Fellow.  The  Society 
of  our  day  bas  greatly  degenerated  :  those  of  the  old  time  would 
be  pleased,  no  doubt,  that  the  glories  of  their  day  should  be 
commemorated.  In  the  early  days  of  the  Society,  there  was  a 
similar  difficulty  about  Graunt,  the  author  of  the  celebrated  work 
on  mortality.  But  their  royal  patron,  'who  never  said  a  foolish 
thing,'  sent  them  a  sharp  message,  and  charged  them  if  they 
found  any  more  such  tradesmen,  they  should  'elect  them  without 
more  ado.' 

Home's  first  pamphlet  was  published  when  he  was  but  twenty- 
one  years  old.  Two  years  afterwards,  being  then  a  Fellow  of  bis 
college,  and  having  seen  more  of  the  world,  he  seems  to  have  felt 
that  his  manner  was  a  little  too  pert.  He  endeavoured,  it  is  said, 
to  suppress  his  first  tract :  and  copies  are  certainly  of  extreme 
rarity.  He  published  the  following  as  his  maturer  view  : 


92  A  BUDGET  OF  PAEADOXES. 


A  fair,  candid,  and  impartial  state  of  the  case  between  Sir 
Isaac  Newton  and  Mr.  HutcLinson.  In  which  is  shown  how 
for  a  system  of  physics  is  capable  of  mathematical  demonstra- 
tion; how  far  Sir  Isaac's,  as  such  a  system,  has  that  demon- 
stration ;  and  consequently,  what  regard  Mr.  Hutchinson's  claim 
may  deserve  to  have  paid  to  it.  By  George  Home,  M.A. 
Oxford,  1753,  8vo. 

It  must  be  remembered  that  the  successors  of  Newton  were 
very  apt  to  declare  that  Newton  had  demonstrated  attraction  as  a 
physical  cause :  he  had  taken  reasonable  pains  to  show  that  he 
did  not  pretend  to  this.  If  any  one  had  said  to  Newton,  I  hold 
that  every  particle  of  matter  is  a  responsible  being  of  vast  intel- 
lect, ordered  by  the  Creator  to  move  as  it  would  do  if  every  other 
particle  attracted  it,  and  gifted  with  power  to  make  its  way  in 
true  accordance  with  that  law,  as  easily  as  a  lady  picks  her  way 
across  the  street ;  what  have  you  to  say  against  it  ? — Newton 
must  have  replied,  Sir !  if  you  really  undertake  to  maintain  this 
as  demonstrable,  your  soul  had  better  borrow  a  little  power  from 
the  particles  of  which  your  body  is  made :  if  you  merely  ask  me 
to  refute  it,  I  tell  you  that  I  neither  can  nor  need  do  it;  for 
whether  attraction  comes  in  this  way  or  in  any  other,  it  comes, 
and  that  is  all  I  have  to  do  with  it. 

The  reader  should  remember  that  the  word  attraction,  as  used 
by  Newton  and  the  best  of  his  followers,  only  meant  a  drawing 
towards,  without  any  implication  as  to  the  cause.  Thus  whether 
they  said  that  matter  attracts  matter,  or  that  young  lady  attracts 
young  gentleman,  they  were  using  one  word  in  one  sense.  Newton 
found  that  the  law  of  the  first  is  the  inverse  square  of  the  dis- 
tance :  I  am  not  aware  that  the  law  of  the  second  has  been 
discovered ;  if  there  be  any  chance,  we  shall  see  it  at  the  year 
1856  in  this  list. 

In  this  point  young  Home  made  a  hit.  He  justly  censures 
those  who  fixed  upon  Newton  a  more  positive  knowledge  of  what 
attraction  is  than  he  pretended  to  have.  'He  has  owned  over 
and  over  he  did  not  know  what  he  meant  by  it — it  might  be  this, 
or  it  might  be  that,  or  it  might  be  anything,  or  it  might  be 
nothing.'  With  the  exception  of  the  nothing  clause,  this  is  true, 
though  Newton  might  have  answered  Home  by  '  Thou  hast  said 
it,' 

(I,thought  everybody  knew  the  meaning  of  '  Thou  hast  said  it :' 
but  I  was  mistaken.  In  three  of  the  evangelists  2v  \systs  is  the 


HOKNE   ON   NEWTON.      WEYMAN   LEE.  93 

answer  to  '  Art  thou  a  king  ?'  The  force  of  this  answer,  as  always 
understood,  is  '  That  is  your  way  of  putting  it.'  The  Puritans, 
who  lived  in  Bible  phrases,  so  understood  it:  and  Walter  Scott, 
who  caught  all  peculiarities  of  language  with  great  effect,  makes 
a  marked  instance, '  Were  you  armed  ? —  I  was  not — I  went  in  my 
calling,  as  a  preacher  of  (rod's  word,  to  encourage  them  that  drew 
the  sword  in  His  cause.  In  other  words,  to  aid  and  abet  the 
rebels,  said  the  Duke.  Thou  hast  spoken  it,  replied  the  prisoner.') 

Again,  Home  quotes  Eowning  as  follows  :  — 

Mr.  Rowning,  pt.  2  p.  5  in  a  nobe,  has  a  very  pretty  conceit  upon 
this  same  subject -of  attraction,  about  every  particle  of  a  fluid  being1 
intrenched  in  three  spheres  of  attraction  and  repulsion,  one  within 
another,  '  the  innermost  of  which  (he  says)  is  a  sphere  of  repulsion, 
which  keeps  them  from  approaching  into  contact ;  the  next,  a  sphere 
of  attraction,  diffused  around  this  of  repulsion,  by  which  the  particles 
are  disposed  to  run  together  into  drops  ;  and  the  outermost  of  all,  a 
sphere  of  repulsion,  whereby  they  repel  each  other,  when  removed  out 
of  the  attraction.'  So  that  between  the  urginys,  and  suUicitations,  of 
one  and  t'other,  a  poor  unhappy  particle  must  ever  be  at  his  wit's  end, 
not  knowing  which  way  to  turn,  or  whom  to  obey  first. 

Rowning  has  here  started  the  notion  which  Boscovich  afterwards 
developed. 

I  may  add  to  what  precedes  that  it  cannot  be  settled  that,  as 
Granger  says,  Desaguliers  was  the  first  who  gave  experimental 
lectures  in  London.  William  Whiston  gave  some,  and  Francis 
Hauksbee  made  the  experiments.  The  prospectus,  as  we  should 
now  call  it,  is  extant,  a  quarto  tract  of  plates  and  descriptions, 
without  date.  Whiston,  in  his  life,  gives  1714  as  the  first  date 
of  publication,  and  therefore,  no  doubt,  of  the  lectures.  Desagu- 
liers removed  to  London  soon  after  1712,  and  commenced  his 
lectures  soon  after  that.  It  will  be  rather  a  nice  point  to  settle 
which  lectured  first;  probabilities  seem  to  go  in  favour  or 
Whiston. 

An  Essay  to  ascertain  the  value  of  leases,  and  annuities  for 
years  and  lives.  By  W[eyman]  L[ee].  London,  1737,  8vo. 

A  valuation  of  Annuities  and  Leases  certain,  for  a  single  life. 
By  Weyman  Lee,  Esq.  of  the  Inner  Temple.  London,  1751, 
8vo.  Third  edition,  177:!. 

Every  branch  of  exact  science  has  its  paradoxer.  The  world  at 
large  cannot  tell  with  certainty  who  is  right  in  such  questions  as 
squaring  the  circle,  &c.  Mr.  Weyrnan  Lee  was  the  assailant  of 


94  A   BUDGET   OF  PARADOXES. 

what  all  who  had  studied  called  demonstration  in  the  question  of 
annuities.  He  can  be  exposed  to  the  world :  for  his  error  arose 
out  of  his  not  being  able  to  see  that  the  whole  is  the  sum  of  all 
its  parts. 

By  an  annuity,  say  of  100£.,  now  bought,  is  meant  that  the 
buyer  is  to  have  for  his  money  lOQl.  in  a  year,  if  he  be  then 
alive,  100L  at  the  end  of  two  years,  if  then  alive,  and  so 
on.  It  is  clear  that  he  would  buy  a  life  annuity  if  he 
should  buy  the  first  100£.  in  one  office,  the  second  in  another, 
and  so  on.  All  the  difference  between  buying  the  whole  from 
one  office,  and  buying  all  the  separate  contingent  payments  at 
different  offices,  is  immaterial  to  calculation.  Mr.  Lee  would 
have  agreed  with  the  rest  of  the  world  about  the  payments  to  be 
made  to  the  several  different  offices,  in  consideration  of  their  several 
contracts  :  but  he  differed  from  every  one  else  about  the  sum  to 
be  paid  to  one,  office.  He  contended  that  the  way  to  value  an 
annuity  is  to  find  out  the  term  of  years  which  the  individual  has 
an  even  chance  of  surviving,  and  to  charge  for  the  life  annuity 
the  value  of  an  annuity  certain  for  that  term. 

It  is  very  common  to  say  that  Lee  took  the  average  life,  or  ex- 
pectation, as  it  is  wrongly  called,  for  his  term :  and  this  I  have 
done  myself,  taking  the  common  story.  Having  exposed  the 
absurdity  of  this  second  supposition,  taking  it  for  Lee's,  in  my 
'Formal  Logic,'  I  will  now  do  the  same  with  the  first. 

A  mathematical  truth  is  true  in  its  extreme  cases.  Lee's  prin- 
ciple is  that  an  annuity  on  a  life  is  the  annuity  made  certain  for 
the  term  within  which  it  is  an  even  chance  the  life  drops.  If, 
then,  of  a  thousand  persons,  500  be  sure  to  die  within  a  year,  and 
the  other  500  be  immortal,  Lee's  price  of  an  annuity  to  any  one 
of  these  persons  is  the  present  value  of  one  payment :  for  one  year 
is  the  term  which  each  one  has  an  even  chance  of  surviving  and 
not  surviving.  But  the  true  value  is  obviously  half  that  of  a 
perpetual  annuity :  so  that  at  5  per  cent.  Lee's  rule  would  give 
less  than  the  tenth  of  the  true  value.  It  must  be  said  for  the 
poor  circle-squarers,  that  they  never  err  so  much  as  this. 

Lee  would  have  said,  if  alive,  that  I  have  put  an  extreme  case  : 
but  any  universal  truth  is  true  in  its  extreme  cases.  It  is  not 
fair  to  bring  forward  an  extreme  case  against  a  person  who  is 
speaking  as  of  usual  occurrences  :  but  it  is  quite  fair  when,  as 
frequently  happens,  the  proposer  insists  upon  a  perfectly  general 
acceptance  of  his  assertion.  And  yet  many  who  go  the  whole  hog 
protest  against  being  tickled  with  the  tail.  Counsel  in  court  are 
good  instances:  they  are  paradoxers  by  trade.  June  13,  1849,  at 


MONTUCLA'S  HISTORY  OF  CIRCLE  SQUARING.  95 

Hertford,  there  was  an  action  about  a  ship,  insured  against  a  total 
loss  :  some  planks  were  saved,  and  the  underwriters  refused  to  pay. 
Mr.  Z.  (for  deft.)  'There  can  be  no  degrees  of  totality;  and  some 
timbers  were  saved.' — L.  C.  B.  'Then  if  the  vessel  were  burned  to 
the  water's  edge,  and  some  rope  saved  in  the  boat,  there  would  be 
no  total  loss.' — Mr.  Z.  'This  is  putting  a  very  extreme  case.' — 
L.  C.  B.  'The  argument  would  go  that  length.'  What  would 
Judge  Z. — as  he  now  is — say  to  the  extreme  case  beginning  some- 
where between  six  planks  and  a  bit  of  rope  ? 

Histoire  des  recherches  sur  la  quadrature  du  cercle.  .  .  .  avec 
une  addition  concernant  les  problemes  de  la  duplication  du 
cube  et  de  la  trisection  de  1'anglo.  Paris,  1754,  12mo.  [By 
Montucla.] 

This  is  the  history  of  the  subject.  It  was  a  little  episode  to 
the  great  history  of  mathematics  by  Montucla,  of  which  the  first 
edition  appeared  in  1758.  There  was  much  addition  at  the  end 
of  the  fourth  volume  of  the  second  edition ;  this  is  clearly  by 
Montucla,  though  the  bulk  of  the  volume  is  put  together,  with 
help  from  Montucla's  papers,  by  Lalande.  There  is  also  a  second 
edition  of  the  history  of  the  quadrature,  Paris,  1831,  8vo, 
edited,  I  think,  by  Lacroix ;  of  which  it  is  the  great  fault  that  it 
makes  hardly  any  use  of  the  additional  matter  just  mentioned.  • 

Montucla  is  an  admirable  historian  when  he  is  writing  from  his 
own  direct  knowledge :  it  is  a  sad  pity  that  he  did  not  tell  us 
when  he  was  depending  on  others.  We  are  not  to  trust  a  quarter 
of  his  book,  and  we  must  read  many  other  books  to  know  which 
quarter.  The  fault  is  common  enough,  but  Montucla's  good 
three-quarters  is  so  good  that  the  fault  is  greater  in  him  than  in 
most  others :  I  mean  the  fault  of  not  acknowledging  ;  for  an 
historian  cannot  read  everything.  But  it  must  be  said  that 
mankind  give  little  encouragement  to  candour  on  this  point. 
Hallam,  in  his  '  History  of  Literature,'  states  with  his  own  usual 
instinct  of  honesty  every  case  in  which  he  depends  upon  others  : 
Montucla  does  not.  And  what  is  the  consequence? — Montucla  is 
trusted,  and  believed  in,  and  cried  up  in  the  bulk  ;  while  the 
smallest  talker  can  lament  that  Hallam  should  be  so  unequal  and 
apt  to  depend  on  others,  without  remembering  to  mention  that 
Hallam  himself  gives  the  information.  As  to  a  universal  history 
of  any  great  subject  being  written  entirely  upon  primary  know- 
ledge, it  is  a  thing  of  which  the  possibility  is  not  yet  proved  by 
an  example.  Delambre  attempted  it  with  astronomy,  and  was 
removed  by  death  before  it  was  finished,  to  say  nothing  of  the 
gaps  he  left. 


96  A   BUDGET   OF   PARADOXES. 

Montucla  was  nothing  of  a  bibliographer,  and  his  descriptions 
of  books  in  the  first  edition  were  insufficient.  The  Abbe  Rive 
fell  foul  of  him,  and  as  the  phrase  is,  gave  it  him.  Montucla 
took  it  with  great  good  humour,  tried  to  mend,  and,  in  his  second 
edition,  wished  his  critic  had  lived  to  see  the  vernis  de  biblio- 
graphe  which  he  had  given  himself. 

I  have  seen  Montucla  set  down  as  an  esprit  fort,  more  than 
once  :  wrongly,  I  think.  When  he  mentions  Barrow's  address  to 
the  Almighty,  he  adds,  '  On  voit,  au  reste,  par  la,  que  Barrow 
etoit  un  pauvre  philosophe  ;  car  il  croyait  en  1'immortalite  de 
1'ame,  et  en  une  Divinite  autre  que  la  nature  universelle.'  This 
is  irony,  not  an  expression  of  opinion.  In  the  book  of  mathe- 
matical recreations  which  Montucla  constructed  upon  that  of 
Ozanam,  and  Ozanam  upon  that  of  Van  Etten,  now  best  known  in 
England  by  Mutton's  similar  treatment  of  Montucla,  there  is  an 
amusing  chapter  on  the  quadrators.  Montucla  refers  to  his  own 
anonymous  book  of  1754  as  a  curious  book  published  by  Jombert. 
He  seems  to  have  been  a  little  ashamed  of  writing  about  circle- 
squarers  :  what  a  slap  on  the  face  for  an  unborn  Budgeteer  I 

Montucla  says,  speaking  of  France,  that  he  finds  three  notions 
prevalent  among  the  cyclometers  :  1.  that  there  is  a  large  reward 
offered  for  success;  2.  that  the  longitude  problem  depends  on 
that  success  ;  3.  that  the  solution  is  the  great  end  and  object  of 
geometry.  The  same  three  notions  are  equally  prevalent  among 
the  same  class  in  England.  No  reward  has  ever  been  offered  by 
the  government  of  either  country.  The  longitude  problem  in 
no  way  depends  upon  perfect  solution  :  existing  approximations 
are  sufficient  to  a  point  of  accuracy  far  beyond  what  can  be 
wanted.  And  geometry,  content  with  what  exists,  has  long  passed 
on  to  other  matters.  Sometimes  a  cyclometer  persuades  a  skipper 
who  has  made  land  in  the  wrong  place  that  the  astronomers  are  in 
fault,  for  using  a  wrong  measure  of  the  circle ;  and  the  skipper 
thinks  it  a  very  comfortable  solution  S  And  this  is  the  utmost 
that  the  proble.ni  ever  has  to  do  with  longitude. 

Antinewtoniamsmus.      By     Cielestino     Cominale,     M.D.    Naples, 
1754  and  1756,  2  vols.  4to. 

The  first  volume  upsets  the  theory  of  light;  the  second 
vacuum,  vis  inertise,  gravitation,  and  attraction.  I  confess  I 
never  attempted  these  big  Latin  volumes,  numbering  450  closely- 
printed  quarto  pages.  The  man  who  slays  Newton  in  a  pamphlet 
is  the  man  for  me.  But  I  will  lend  them  to  anybody  who  will 


REWARD   FOR   QUADRATURE.  97 

give  security,  himself  in  500£.,  and  two  sureties  in  2501.  each,  that 
he  will  read  them  through,  and  give  a  full  abstract ;  and  I  will 
not  exact  security  for  their  return.  I  have  never  seen  any 
mention  of  this  book :  it  has  a  printer,  but  not  a  publisher,  as 
happens  with  so  many  unrecorded  books. 

1755.  The  French  Academy  of  Sciences  came  to  the  deter- 
mination not  to  examine  any  more  quadratures  or  kindred 
problems.  This  was  the  consequence,  no  doubt,  of  the  publication 
of  Montucla's  book  :  the  time  was  well  chosen  ;  for  that  book  was 
a  full  justification  of  the  resolution.  The  Eoyal  Society  followed 
the  same  course,  I  believe,  a  few  years  afterwards.  When  our 
Board  of  Longitude  was  in  existence,  most  of  its  time  was  con- 
sumed in  listening  to  schemes,  many  of  which  included  the 
quadrature  of  the  circle.  It  is  certain  that  many  quadrators  have 
imagined  the  longitude  problem  to  be  connected  with  theirs  :  and 
no  doubt  the  notion  of  a  reward  being  offered  by  Government  for 
a  true  quadrature  is  a  result  of  the  reward  offered  for  the  longi- 
tude. Let  it  also  be  noted  that  this  longitude  reward  was  not 
a  premium  upon  excogitation  of  a  mysterious  difficulty.  The 
legislature  was  made  to  know  that  the  rational  hopes  of  the 
problem  were  centred  in  the  improvement  of  the  lunar  tables  and 
the  improvement  of  chronometers.  To  these  objects  alone,  and 
by  name,  the  offer  was  directed :  several  persons  gained  rewards 
for  both ;  and  the  offer  was  finally  repealed. 

Fundamentals  Figura  Georaetrica,  primas  tantum  lineas  circuli 
quadrature  possibilitatis  ostendens.  By  Niels  Erichsen 
(Nicolaus  Ericius),  shipbuilder,  of  Copenhagen.  Copenhagen, 
1755,  12mo. 

This  was  a  gift  from  my  oldest  friend  who  was  not  a  relative, 
Dr.  Samuel  Maitland  of  the  '  Dark  Ages.'  He  found  it  among 
his  books,  and  could  not  imagine  how  he  came  by  it :  I  could 
have  told  him.  He  once  collected  interpretations  of  the  Apo- 
calypse :  and  auction  lots  of  such  books  often  contain  quadratures. 
The  wonder  is  he  never  found  more  than  one. 

The  quadrature  is  not  worth  notice.  Erichsen  is  the  only 
squarer  I  have  met  with  who  has  distinctly  asserted  the  particulars 
of  that  reward  which  has  been  so  frequently  thought  to  have  been 
offered  in  England.  He  says  that,  in  1747,  the  Eoyal  Society,  on 
the  2nd  of  June,  offered  to  give  a  large  reward  for  the  quadrature  of 
the  circle  and  a  true  explanation  of  magnetism,  in  addition  to 
30,000^.  previously  promised  for  the  same.  I  need  hardly  say  that 

ir 


98  A  BUDGET   OE  PARADOXES. 

the  Royal  Society  had  not  30,000£.  at  that  time,  and  would  not,  if 
it  had  had  such  a  sum,  have  spent  it  on  the  circle,  nor  on  magnetic 
theory  ;  nor  would  it  have  coupled  the  two  things.  On  this  book, 
see  Notes  and  Queries,  1st  S.  xii.  306.  Perhaps  Erichsen  meant 
that  the  30,000£.  had  been  promised  by  the  Government,  and  the 
addition  by  the  Eoyal  Society. 

October  8,  1866.  I  receive  a  letter  from  a  cyclometer  who 
understands  that  a  reward  is  offered  to  any  one  who  will  square 
the  circle,  and  that  all  competitors  are  to  send  their  plans  to  me. 
The  hoaxers  have  not  yet  failed  out  of  the  land. 

Theoria  Philosophise  Naturalis  redacta  ad  unicam  legem  virium 
in  natura  existentium.  Editio  Veneta  prima.  By  Roger  Joseph 
Boscovich.  Venice,  1763,  4to. 

The  first  edition  is  said  to  be  of  Vienna,  1758.  This  is  a 
celebrated  work  on  the  molecular  theory  of  matter,  grounded  on 
the  hypothesis  of  spheres  of  alternate  attraction  and  repulsion. 
Boscovich  was  a  Jesuit  of  varied  pursuit.  During  his  measure- 
ment of  a  degree  of  the  meridian,  while  on  horseback  or  waiting 
for  his  observations,  he  composed  a  Latin  poem  of  about  five 
thousand  verses  on  eclipses,  with  notes,  which  he  dedicated  to  the 
Eoyal  Society  :  '  De  Solis  et  Lunse  defectibus,'  London,  Millar 
and  Dodsley,  1760,  4to. 

Traite  de  paix  entre  DCS  Cartes  et  Newton,  precede  des  vies 
littcraires  de  ces  deux  chefs  de  la  physique  moderne.  .  .  .  By 
Aime  Henri  Paulian.  Avignon,  1763,  12mo. 

I  have  had  these  books  for  many  a  year  without  feeling  the 
least  desire  to  see  how  a  lettered  Jesuit  would  atone  Descartes 
and  Newton.  On  looking  at  my  two  volumes,  I  find  that  one 
contains  nothing  but  the  literary  life  of  Des  Cartes  ;  the  other 
nothing  but  the  literary  life  of  Newton.  The  preface  indicates 
more  :  and  Watt  mentions  three  volumes.  I  dare  say  the  first 
two  contain  all  that  is  valuable.  On  looking  more  attentively  at 
the  two  volumes,  I  find  them  both  readable  and  instructive ;  the 
account  of  Newton  is  far  above  that  of  Voltaire,  but  not  so 
popular.  But  he  should  not  have  said  that  Newton's  family 
came  from  Newton  in  Ireland.  Sir  Rowland  Hill  gives  fourteen 
Newtons  in  Ireland :  twice  the  number  of  the  cities  that  con- 
tended for  the  birth  of  Homer  may  now  contend  for  the  origin  of 
Newton,  on  the  word  of  Father  Paulian. 


BAILLY'S  LETTERS  TO  VOLTAIRE.  99 


Philosophical  Essays,  in  three  parts.  By  B.  Lovett,  Lay 
Clerk  of  the  Cathedral  Church  of  Worcester.  Worcester,  1766, 
8vo. 

The  Electrical  Philosopher:  containing  a  new  system  of 
physics  founded  upon  the  principle  of  an  universal  Plenum 
of  elementary  fire  .  .  .  By  R.  Lovett.  Worcester,  1774,  8vo. 

Mr.  Lovett  was  one  of  those  ether  philosophers  who  bring  in 
elastic  fluid  as  an  explanation  by  imposition  of  words,  without 
deducing  any  one  phenomenon  from  what  we  know  of  it.  And 
yet  he  says  that  attraction  has  received  no  support  from  geome- 
try ;  though  geometry,  applied  to  a  particular  law  of  attraction, 
had  shown  how  to  predict  the  motions  of  the  bodies  of  the  t^olar 
system.  He,  and  many  of  his  stamp,  have  not  the  least  idea  of 
the  confirmation  of  a  theory  by  accordance  of  deduced  results 
with  observation  posterior  to  the  theory. 

Lettres  sur  1'Atlantide  de  Platon,  et  sur  1'ancien  Histoire  de 
1' Asie,  pour  servir  de  suite  aux  lettres  sur  1'origine  des  Sciences, 
adressees  a  M.  de  Voltaire,  par  M.  Bailly.  London  and  Paris, 
'1779,  8vo. 

I  might  enter  here  all  Bailly's  histories  of  astronomy.  The 
paradox  which  runs  through  them  all  more  or  less,  is  the  doctrine 
that  astronomy  is  of  immense  antiquity,  coming  from  some 
forgotten  source,  probably  the  drowned  island  of  Plato,  peopled 
by  a  race  whom  Bailly  makes,  as  has  been  said,  to  teach  us 
everything  except  their  existence  and  their  name.  These  books, 
the  first  scientific  histories  which  belong  to  readable  literature, 
made  a  great  impression  by  power  of  style  :  Delambre  created  a 
strong  reaction,  of  injurious  amount,  in  favour  of  history  founded 
on  contemporary  documents,  which  early  astronomy  cannot 
furnish.  These  letters  are  addressed  to  Voltaire,  and  continue 
the  discussion.  There  is  one  letter  of  Voltaire,  being  the  fourth, 
dated  Feb.  27,  1777,  and  signed  '  le  vieux  malade  de  Ferney,  V. 
puer  centum  annorum.'  Then  begin  Bailly's  letters,  from 
January  16  to  May  12,  1778.  From  some  ambiguous  expressions 
in  the  Preface,  it  would  seem  that  these  are  fictitious  letters,  sup- 
posed to  be  addressed  to  Voltaire  at  their  dates.  Voltaire  went 
to  Paris  February  10,  1778,  and  died  there  May  30.  Nearly  all 
this  interval  was  his  closing  scene,  and  it  is  very  unlikely  that 
Bailly  would  have  troubled  him  with  these  letters. 


H  a 


100  A  BUDGET   OF   PAEADOXES. 

An  inquiry  into  the  cause  of  motion,  or  a  general  theory  of 
physics.     By  S.  Miller.     London,  1781,  4to. 

Newton  all  wrong :  matter  consists  of  two  kinds  of  particles, 
one  inert,  the  other  elastic  and  capable  of  expanding  themselves 
ad  infinitum. 

Des  Erreurs  et  de  la  Verite,  ou  les  hommes  rappeles  au  prin- 
cipe  universel  de  la  science ;  ouvrage  dans  lequel,  en  faisant 
remarquer  aux  observateurs  1'incertitude  de  leurs  recherches, 
et  leurs  meprises  continuelles,  on  leur  indique  la  route  qu'ils 
auroient  du.  suivre,  pour  acquerir  1'evidence  physique  sur 
1'origine  du  bien  et  du  mal,  sur  l'homme,  sur  la  nature  matcrielle, 
et  la  nature  sacree ;  sur  la  base  des  gouvernements  politiques, 
sur  1'autorite  des  souverains,  sur  la  justice  civile  et  criininellc, 
sur  les  sciences,  les  langues,  et  les  arts.  Par  un  Ph.  .  .  . 
Inc.  ...  A  Edimbourg.  1782.  Two  vols.  8vo. 

This  is  the  famous  work  of  Louis  Claude  de  Saint-Martin 
(1743-1803),  for  whose  other  works,  vagaries  included,  the  reader 
must  look  elsewhere  :  among  other  things,  he  was  a  translator  of 
Jacob  Behrnen.  The  title  promises  much,  and  the  writer  has 
smart  thoughts  now  and  then ;  but  the  whole  is  the  wearisome 
omniscience  of  the  author's  day  and  country,  which  no  reader  of 
our  time  can  tolerate.  Not  that  we  dislike  omniscience ;  but 
we  have  it  of  our  own  country,  both  home-made  and  imported  ; 
and  fashions  vary.  But  surely  there  can  be  but  one  omniscience  ? 
Must  a  man  have  but  one  wife  ?  Nay,  may  not  a  man  have  a 
new  wife  while  the  old  one  is  living  ?  There  was  a  famous 
instrumental  professor  forty  years  ago,  who  presented  a  friend  to 

Madame .     The   friend  started,   and  looked  surprised ;  for, 

not  many  weeks  before,  he  had  been  presented  to  another  lady, 
with  the  same  title,  at  Paris.  The  musician  observed  his 

surprise,  and  quietly  said,   '  Celle-ci  est  Madame de  Lon- 

dres.'  In  like  manner  we  have  a  London  omniscience  now 
current,  which  would  make  any  one  start  who  only  knew  the  old 
French  article. 

The  book  was  printed  at  Lyon,  but  it  was  a  trick  of  French 
authors  to  pretend  to  be  afraid  of  prosecution :  it  made  a  book 
look  wicked-like  to  have  a  feigned  place  of  printing,  and  stimu- 
lated readers.  A  Government  which  had  undergone  Voltaire 
would  never  have  drawn  its  sword  upon  quiet  Saint-Martin.  To 
make  himself  look  still  worse,  he  was  only  ph[ilosophe]  Inc.  .  .  , 
which  is  generally  read  Inconnu,  but  sometimes  Incredule : 


SAINT-MARTIN.  101 

most  likely  the  ambiguity  was  intended.  There  is  an  awful 
paradox  about  the  book,  which  explains,  in  part,  its  leaden  same- 
ness. It  is  all  about  Vhomme,  Vhomme,  Vhomme,  except  as  much 
as  treats  of  les  homines,  les  hommes,  les  hommes ;  but  not  one 
single  man  is  mentioned  by  name  in  its  500  pages.  It  reminds 
one  of 

Water,  water,  everywhere, 

And  not  a  drop  to  drink. 

Not  one  opinion  of  any  other  man  is  referred  to,  in  the  way  of 
agn-emcnt  or  of  opposition.  Not  even  a  town  is  mentioned  : 
there  is  nothing  which  brings  a  capital  letter  into  the  middle  of  a 
sentence,  except,  by  the  rarest  accident,  siich  a  personification  as 
Justice.  A  likely  book  to  want  an  Edimbourg  godfather ! 

Saint-Martin  is  great  in  mathematics.  The  number  four 
essentially  belongs  to  straight  lines,  and  nine  to  curves.  The 
object  of  a  straight  line  is  to  perpetuate  ad  infinitum  the  pro- 
duction of  a  point  from  which  it  emanates.  A  circle  O  bounds 
the  production  of  all  its  radii,  tends  to  destroy  them,  and  is  in 
some  sort  their  enemy.  How  is  it  possible  that  things  so  distinct 
should  not  be  distinguished  in  their  number  as  well  as  in  their 
action  ?  If  this  important  observation  had  been  made  earlier, 
immense  trouble  would  have  been  saved  to  the  mathematicians, 
who  would  have  been  prevented  from  searching  for  a  common 
measure  to  lines  which  have  nothing  in  common.  But,  though 
all  straight  lines  have  the  number  four,  it  must  not  be  supposed 
that  they  are  all  equal,  for  a  line  is  the  result  of  its  law  and  its 
number  ;  but  though  both  are  the  same  for  all  lines  of  a  sort, 
they  act  differently,  as  to  force,  energy,  and  duration,  in  different 
individuals ;  which  explains  all  differences  of  length,  &c.  I 
congratulate  the  reader  who  understands  this  ;  and  I  do  not  pity 
the  one  who  does  not. 

Saint-Martin  and  his  works  are  now  as  completely  forgotten  as 
if  they  had  never  been  born,  except  so  far  as  this,  that  some  one 
may  take  up  one  of  the  works  as  of  heretical  character,  and  lay  it 
down  in  disappointment,  with  the  reflection  that  it  is  as  dull  as 
orthodoxy.  For  a  person  who  was  once  in  some  vogue,  it  would 
be  difficult  to  pick  out  a  more  fossil  writer,  from  Aa  to  Zypoeus, 
except, — though  it  is  unusual  for  (, — )  to  represent  an  interval  of 
more  than  a  year — his  unknown  opponent.  This  opponent,  in  the 
very  year  of  the  '  Des  Erreurs  .  .  .  .'  published  a  book  in  two 
parts  with  the  same  fictitious  place  of  printing ; 


102  A   BUDGET   OF   PARADOXES. 


Tableau  Naturel  des  Rapports  qui  existent  entre  Dieu,  1'Horame, 
et  1'Univers.     A  Edimbourg,  1782,  8vo. 

There  is  a  motto  from  the  Des  Erreurs  itself,  '  Expliquer  les 
choses  par  I'homme,  et  non  1'homme  par  les  choses.  Des  Erreurs 
et  de  la  Verite,  par  un  PH.  .  .  .  INC.  .  .  .,  p.  9.'  This  work  is  set 
down  in  various  catalogues  and  biographies  as  written  by  the 
PH.  .  .  .  INC.  .  .  .  himself.  But  it  is  not  usual  for  a  writer  to 
publish  two  works  in  the  same  year,  one  of  which  takes  a  motto 
from  the  other.  And  the  second  work  is  profuse  in  capitals  and 
italics,  and  uses  Hebrew  learning :  its  style  differs  much  from  the 
first  work.  The  first  work  sets  out  from  man,  and  has  nothing 
to  do  with  Grod :  the  second  is  religious  and  raps  the  knuckles  of 
the  first  as  follows : — '  Si  nous  voulons  nous  preserver  de  toutes 
les  illusions,  et  surtout  des  amorces  de  1'orgueil  par  lesquelles 
1'homme  est  si  souvent  seduit,  ne  prenons  jamais  les  homines, 
mais  toujours  Dieu  pour  notre  terme  de  comparaison.'  The  first 
uses  four  and  nine  in  various  ways,  of  which  I  have  quoted  one  : 
the  second  says,  '  Et  ici  se  trouve  deja  ime  explication  des 
nombres  quatre  et  neuf,  qui  ont  peu  embarrasse  dans  1'ouvrage  deja 
cite.  L'homme  s'est  egare  en  allant  de  quatre  a  neuf  .  .  .  .' 
The  work  cited  is  the  Erreurs,  &c.,  and  the  citation  is  in  the 
motto,  which  is  the  text  of  the  opposition  sermon. 

Method  to  discover  the  difference  of  the  earth's  diameters ; 
proving  its  true  ratio  to  be  not  less  variable  than  as  45  is  to  46, 
and  shortest  in  its  pole's  axis  174  miles  .  .  .  likewise  a  method 
for  fixing  an  universal  standard  for  weights  and  measures.  By 
Thomas  Williams.  London,  1788,  8vo. 

Mr.  Williams  was  a  paradoxer  in  his  day,  and  proposed  what 
was,  no  doubt,  laughed  at  by  some.  He  proposed  the  sort  of  plan 
which  the  French — independently  of  course — carried  into  effect  a 
few  years  after.  He  would  have  the  52nd  degree  of  latitude 
divided  into  100,000  parts  and  each  part  a  geographical  yard. 
The  geographical  tun  was  to  be  the  cube  of  the  geographical 
yard  filled  with  sea-water  taken  some  leagues  from  land.  All 
multiples  and  subdivisions  were  to  be  decimal. 

I  was  beginning  to  look  up  those  who  had  made  similar 
proposals,  when  a  learned  article  .on  the  proposal  of  a  metrical 
system  came  under  my  eye  in  the  Times  of  Sept.  15,  1863.  The 
author  cites  Mouton,  who  would  have  the  minute  of  a  degree 
divided  into  10,000  virgulce;  James  Cassini,  whose  foot  was  to  be 


PAINE— WOLLSTONECE  AFT— PAKR.  103 

six  thousandths  of  a  minute ;  and  Paucton,  whose  foot  was  the 
400,000th  of  a  degree.  I  have  verified  the  first  and  third  state- 
ments ;  surely  the  second  ought  to  be  the  six-thousandth. 

An  inquiry  into  the  Copernican  system  .  .  .  wherein  it  is 
proved,  in  the  clearest  manner,  that  the  earth  has  only  her 
diurnal  motion  .  .  .  with  an  attempt  to  point  out  the  only  true 
way  whereby  mankind  can  receive  any  real  benefit  from  the 
study  of  the  heavenly  bodies.  By  John  Cunningham.  London, 
]  789,  8vo. 

The  '  true  way '  appears  to  be  the  treatment  of  heaven  and 
earth  as  emblematical  of  the  Trinity. 

Cosmology.  An  inquiry  into  the  cause  of  what  is  called  gra- 
vitation or  attraction,  in  which  the  motions  of  the  heavenly 
bodies,  and  the  preservation  and  operations  of  all  nature,  are 
deduced  from  an  universal  principle  of  efflux  and  reflux.  By 
T.  Vivian,  vicar  of  Corn  wood,  Devon.  Bath,  1792,  12mo. 

Attraction,  an  influx  of  matter  to  the  sun  ;  centrifugal  force, 
the  solar  rays ;  cohesion,  the  pressure  of  the  atmosphere.  The 
confusion  about  centrifugal  force,  so  called,  as  demanding  an 
external  agent,  is  very  common. 

The  rights  of  MAN,  being  an  answer    to  Mr.   Burke's  attack  on 

the    French   Revolution.     By  Thomas   Paine.     In   two   parts. 

1791-1792.     8vo.     (Various  editions.) 
A    vindication  of    the    rights     of    WOMAN,   with    strictures    on 

political  and  moral  subjects.     By  Mary  Wollstonecraft.     1792. 

8vo. 
A   sketch   of  the   rights   of  BOYS    and   GIRLS.      By    Launcelot 

Light,    of  Westminster    School ;    and    Laetitia    Lookabout,    of 

Queen's   Square,    Bloomsbury.       [By   the   Rev.   Samuel  Parr, 

LL.D.]     1792.    8vo.  (pp.  64). 

When  did  we  three  meet  before  ?  The  first  work  has  sunk  into 
oblivion :  had  it  merited  its  title,  it  might  have  lived.  It  is  what 
the  French  call  a  piece  de  circonstance ;  it  belongs  in  time  to  the 
French  Revolution,  and  in  matter  to  Burke's  opinion  of  that 
movement.  Those  who  only  know  its  name  think  it  was  really 
an  attempt  to  write  a  philosophical  treatise  on  what  we  now  call 
socialism.  Silly  government  prosecutions  gave  it  what  it  never 
could  have  got  for  itself. 

Mary  Wollstonecraft  seldom  has  her  name  spelt  right.  I 
suppose  the  0  !  O !  character  she  got  made  her  Woolstonecraft. 


104  A  BUDGET   OF   PARADOXES. 

Watt  gives  double  insinuation,  for  his  cross-reference  sends  us  to 
Goodwin.  No  doubt  the  title  of  the  book  was  an  act  of  disciple- 
ship  to  Paine's  '  Rights  of  Man ' ;  but  this  title  is  very  badly 
chosen.  The  book  was  marred  by  it,  especially  when  the  authoress 
and  her  husband  assumed  the  right  of  dispensing  with  legal 
sanction  until  the  appfoach  of  offspring  brought  them  to  a  sense 
of  their  child's  interest.  Not  a  hint  of  such  a  claim  is  found  in 
the  book,  which  is  mostly  about  female  education.  The  right 
claimed  for  woman  is  to  have  the  education  of  a  rational  human 
being,  and  not  to  be  considered  as  nothing  but  woman  throughout 
youthful  training.  The  maxims  of  Mary  Wollstonecraft  are  now, 
though  not  derived  from  her,  largely  followed  in  the  education  of 
girls,  especially  in  home  education :  just  as  many  of  the  political 
principles  of  Tom  Paine,  again  not  derived  from  him,  are  the 
guides  of  our  actual  legislation.  I  remember,  forty  years  ago, 
an  old  lady  who  used  to  declare  that  she  disliked  girls  from  the 
age  of  sixteen  to  five-and-twenty.  '  They  are  full,'  said  she,  '  of 
femalities.'  She  spoke  of  their  behaviour  to  women  as  well  as  to 
men.  She  would  have  been  shocked  to  know  that  she  was  a 
follower  of  Mary  Wollstonecraft,  and  had  packed  half  her  book 
into  one  sentence. 

The  third  work  is  a  satirical  attack  on  Mary  Wollstonecraft  and 
Tom  Paine.  The  details  of  the  attack  would  convince  any  one 
that  neither  has  anything  which  would  now  excite  reprobation. 
It  is  utterly  unworthy  of  Dr.  Parr,  and  has  quite  disappeared 
from  lists  of  his  works,  if  it  were  ever  there.  That  it  was  written 
by  him  I  take  to  be  evident,  as  follows.  Nichols,  who  could  not 
fail  to  know,  says  (Anecd.,  vol.  ix.  p.  120):  'This  is  a  playful 
essay  by  a  first-rate  scholar,  who  is  elsewhere  noticed  in  this 
volume,  but  whose  name  I  shall  not  bring  forward  on  so  trifling 
an  occasion.'  Who  the  scholar  was  is  made  obvious  by  Master 
Launcelot  being  made  to  talk  of  Bellendenus.  Further,  the 
same  boy  is  made  to  say,  '  Let  Dr.  Parr  lay  his  hand  upon  his 
heart,  if  his  conscience  will  let  him,  and  ask  himself  how  many 
thousands  of  waggon-loads  of  this  article  [birch]  he  has  cruelly 
misapplied.'  How  could  this  apply  to  Parr,  with  his  handful  of 
private  pupils,  and  no  reputation  for  severity  ?  Any  one  except 
himself  would  have  called  on  the  head-master  of  Westminster  or 
Eton.  I  doubt  whether  the  name  of  Parr  could  be  connected 
with  the  rod  by  anything  in  print,  except  the  above  and  an 
anecdote  of  his  pupil,  Tom  Sheridan.  The  Doctor  had  dressed 
for  a  dinner  visit,  and  was  ready  a  quarter  of  an  hour  too  soon  to 
set  off.  « Tom,'  said  he,  « I  think  I  had  better  whip  you  now ; 


SAMUEL   PARR.  105 

you  are  sure  to  do  something  while  I  am  out.' — '  I  wish  you  would, 
sir ! '  said  the  boy  ;  '  it  would  be  a  letter  of  licence  for  the  whole 
evening-.'  The  Doctor  saw  the  force  of  the  retort :  my  two 
tutelaries  will  see  it  by  this  time.  They  paid  in  advance  ;  and  I 
have  given  liberal  interpretation  to  the  order. 

The  following  story  of  Dr.  Parr  was  told  me  and  others,  about 
1829,  by  the  late  Leonard  Homer,  who  knew  him  intimately. 
Parr  was  staying  in  a  house  full  of  company,  I  think  in  the 
north  of  England.  Some  gentlemen  from  America  were  among 
the  guests,  and  after  dinner  they  disputed  some  of  Parr's  asser- 
tions or  arguments.  So  the  Doctor  broke  out  with  '  Do  you 
know  what  country  you  come  from  ?  You  come  from  the  place 
to  which  we  used  to  send  our  thieves ! '  This  made  the  host 
angry,  and  he  gave  Parr  such  a  severe  rebuke  as  sent  him  irom 
the  room  in  ill-humour.  The  rest  walked  on  the  lawn,  amusing 
the  Americans  with  sketches  of  the  Doctor.  There  was  a  dark 
cloud  overhead,  and  from  that  cloud  presently  came  a  voice 
which  called  Tham  (Parr-lisp  for  Sam).  The  company  were 
astonished  for  a  moment,  but  thought  the  Doctor  was  calling  his 
servant  in  the  house,  and  that  the  apparent  direction  was  an 
illusion  arising  out  of  inattention.  But  presently  the  sound  was 
repeated,  certainly  from  the  cloud, 

And  nearer,  clearer,  deadlier  than  before. 

There  was  now  a  little  alarm  :  where  could  the  Doctor  have  got 
to  ?  They  ran  to  his  bedroom,  and  there  they  discovered  a 
sufficient  rather  than  satisfactory  explanation.  The  Doctor  had 
taken  his  pipe  into  his  bedroom,  and  had  seated  himself,  in  sulky 
mood,  upon  the  higher  bar  of  a  large  and  deep  old-fashioned 
grate  with  a  high  mantelshelf.  Here  he  had  tumbled  backwards, 
and  doubled  himself  up  between  the  bars  and  the  back  of  the 
grate.  He  was  fixed  tight,  and  when  he  called  for  help,  he  could 
only  throw  his  voice  up  the  chimney.  The  echo  from  the  cloud 
was  the  warning  which  brought  his  friends  to  the  rescue. 

Days  of  political  paradox  were  coming,  at  which  we  now  stare. 
Cobbett  said,  about  1830,  in  earnest,  that  in  the  country  every 
man  who  did  not  take  off  his  hat  to  the  clergyman  was  suspected, 
and  ran  a  fair  chance  of  having  something  brought  against  him. 
I  heard  this  assertion  canvassed,  when  it  was  made,  in  a  party  of 
elderly  persons.  The  Radicals  backed  it,  the  old  Tories  rather 
denied  it,  but  in  a  way  which  satisfied  me  they  ought  to  have 
denied  it  less  if  they  could  not  deny  it  more.  But  it  must  be 
said  that  the  Governments  stopped  far  short  of  what  their 


106  A  BUDGET   OF   PARADOXES. 

partisans  would  have  had  them  do.  All  who  know  Robert 
Robinson's  very  quiet  assault  on  church-made  festivals  in  hi 
'  History  and  Mystery  of  Good  Friday '  (1777)  will  hear  or 
remember  with  surprise  that  the  British  Critic  pronounced  it 
a  direct,  unprovoked,  and  malicious  libel  on  the  most  sacred 
institutions  of  the  national  Church.  It  was  reprinted  again  and 
again:  in  1811  it  was  in  a  cheap  form  at  6s  6^.  a  hundred. 
When  the  Jacobin  day  came,  the  State  was  really  in  a  fright : 
people  thought  twice  before  they  published  what  would  now  be 
quite  disregarded.  I  examined  a  quantity  of  letters  addressed  to 
George  Dyer  (Charles  Lamb's  G.D.)  and  what  between  the  auto- 
graphs of  Thelwall,  Hardy,  Home  Tooke,  and  all  the  rebels, 
put  together  a  packet  which  produced  five  guineas,  or  there- 
abouts, for  the  widow.  Among  them  were  the  following  verses, 
sent  by  the  author — who  would  not  put  his  name,  even  in  a 
private  letter,  for  fear  of  accidents — for  consultation  whether  they 
could  safely  be  sent  to  an  editor  :  and  they  were  not  sent.  The 
occasion  was  the  public  thanksgiving  at  St.  Paul's  for  the  naval 
victories,  December  19,  1797. 

God  bless  me  !  what  a  thing  ! 
Have  you  heard  that  the  King 

Goes  to  St.  Paul's  ? 
Good  Lord  !  and  when  he's  there, 
He'll  roll  his  eyes  in  prayer, 
To  make  poor  Johnny  stare 

At  this  fine  thing. 

No  doubt  the  plan  is  wise 
To  blind  poor  Johnny's  eyes 

By  this  grand  show ; 
For  should  he  once  suppose 
That  he's  led  by  the  nose, 
Down  the  whole  fabric  goes, 

Church,  lords,  and  king. 

As  he  shouts  Duncan's  praise, 
Mind  how  supplies  they'll  raise 

In  wondrous  haste. 
For  while  upon  the  sea 
We  gain  one  victory, 
John  still  a  dupe  will  be 

And  taxes  pay. 

Till  from  his  little  store 
Three-fourths  or  even  more 
Goes  to  the  Crown. 


WILLIAM   HONE'S   TRIALS,  107 

Ah,  John  !  you  little  think 
How  fast  we  downward  sink 
And  touch  the  fatal  brink 
At  which  we're  slaves. 

I  would  have  indicted  the  author  for  not  making  his  thirds 
and  sevenths  rhyme.  As  to  the  rhythm,  it  is  not  much  better 
than  what  the  French  sang  in  the  Calais  theatre,  when  the  Duke 
of  Clarence  took  over  Louis  XVIII.  in  1814. 

God  save  noble  Clarence, 

Who  brings  our  king  to  France  ; 

God  save  Clarence  ! 
He  maintains  the  glory 
Of  the  British  navy. 
&c.  &c. 

Perhaps  had  this  been  published,  the  Government  would  have 
assailed  it  as  a  libel  on  the  church  service.  They  got  into  the 
way  of  defending  themselves  by  making  libels  on  the  Church,  of 
what  were  libels,  if  on  anything,  on  the  rulers  of  the  State  ;  until 
the  celebrated  trials  of  Hone  settled  the  point  for  ever,  and 
established  that  juries  will  not  convict  for  one  offence,  even 
though  it  have  been  committed,  when  they  know  the  prosecution 
is  directed  at  another  offence  and  another  intent. 

The  results  of  Hone's  trials  (William  Hone,  1779-1842)  are 
among  the  important  constitutional  victories  of  our  century.  He 
published  parodies  on  the  Creeds,  the  Lord's  Prayer,  the  Cate- 
chism, &c.,  with  intent  to  bring  the  Ministry  into  contempt : 
everybody  knew  that  was  his  purpose.  The  Government  indicted 
him  for  impious,  profane,  blasphemous  intent,  but  not  for 
seditious  intent.  They  hoped  to  wear  him  out  by  proceeding  day 
by  day.  December  18,  1817,  they  hid  themselves  under  the 
Lord's  Prayer,  the  Creed,  and  the  Commandments ;  December  1 9, 
under  the  Litany  ;  December  20,  under  the  Athanasian  Creed, 
an  odd  place  for  shelter  when  they  could  not  find  it  in  the  previous 
places.  Hone  defended  himself  for  six,  seven,  and  eight  hours  on 
the  several  days:  and  the  jury  acquitted  him  in  15,  105,  and  20 
minutes.  In  the  second  trial  the  offence  was  laid  both  as  pro- 
fanity and  as  sedition,  which  seems  to  have  made  the  jury  hesitate. 
And  they  probably  came  to  think  that  the  second  count  was  false 
pretence :  but  the  length  of  their  deliberation  is  a  satisfactory 
addition  to  the  value  of  the  whole.  In  the  first  trial  the  Attorney- 
General  (Shepherd)  had  the  impudence  to  say  that  the  libel 
had  nothing  of  a  political  tendency  about  it,  but  was  avowedly 


108  A   BUDGET   OF  PAEADOXES 

set  off  against  the  religion  and  worship  of  the  Church  of  England. 
The  whole  is  political  in  every  sentence ;  neither  more  nor  less 
political  than  the  following,  which  is  part  of  the  parody  on  the 
Catechism.  '  What  is  thy  duty  towards  the  Minister  ?  My  duty 
towards  the  Minister  is,  to  trust  him  as  much  as  I  can  ;  to  honour 
him  with  all  my  words,  with  all  my  bows,  with  all  my  scrapes, 
and  with  all  my  cringes ;  to  flatter  him  ;  to  give  him  thanks ;  to 
give  up  my  whole  soul  to  him ;  to  idolize  his  name,  and  obey  his 
word,  and  serve  him  blindly  all  the  days  of  his  political  life.' 
And  the  parody  on  the  Creed  begins,  '  I  believe  in  George,  the 
Regent  almighty,  maker  of  new  streets  and  Knights  of  the  Bath.' 
This  is  what  the  Attorney- General  said  had  nothing  of  a  political 
tendency  about  it.  But  this  was  on  the  first  trial :  Hone 
was  not  known.  The  first  day's  trial  was  under  Justice  Abbott 
(afterwards  C.  J.  Tenterden).  It  was  perfectly  understood,  when 
Chief  Justice  Ellenborough  appeared  in  Court  on  the  second  day, 
that  he  was  very  angry  at  the  first  result,  and  put  his  junior  aside 
to  try  his  own  rougher  dealing.  But  Hone  tamed  the  lion.  An 
eye-witness  told  me  that  when  he  implored  of  Hone  not  to  detail 
his  own  father  Bishop  Law's  views  on  the  Athanasian  Creed,  which 
humble  petition  Hone  kindly  granted,  he  held  by  the  desk  for 
support.  And  the  same  when — which  is  not  reported — the 
Attorney-General  appealed  to  the  Court  for  protection  against  a 
stinging  attack  which  Hone  made  on  the  Bar :  he  held  on,  and 
said,  '  Mr.  Attorney,  what  can  I  do  ! '  I  was  a  boy  of  twelve  years 
old,  but  so  strong  was  the  feeling  of  exultation  at  the  verdicts 
that  boys  at  school  were  not  prohibited  from  seeing  the  parodies, 
which  would  have  been  held  at  any  other  time  quite  unfit  to 
meet  their  eyes.  I  was  not  able  to  comprehend  all  about  the 
Lord  Chief  Justice  until  I  read  and  heard  again  in  after  years. 
In  the  meantime,  Joe  Miller  had  given  me  the  story  of  the 
leopard  which  was  sent  home  on  board  a  ship  of  war,  and  was  in 
two  days  made  as  docile  as  a  cat  by  the  sailors.  '  You  have  got 
that  fellow  well  under,'  said  an  officer.  'Lord  bless  your  honour !' 
said  Jack,  '  if  the  Emperor  of  Marocky  would  send  us  a  cock 
rhinoceros,  we'd  bring  him  to  his  bearings  in  no  time  ! '  When  I 
came  to  the  subject  again,  it  pleased  me  to  entertain  the  question 
whether,  if  the  Emperor  had  sent  a  cock  rhinoceros  to  preside  on 
the  third  day  in  the  King's  Bench,  Hone  would  have  mastered 
him :  I  forget  how  I  settled  it.  There  grew  up  a  story  that  Hone 
caused  Lord  Ellenborough's  death,  but  this  could  not  have  been 
true.  Lord  Ellenborough  resigned  his  seat  in  a  few  months,  and 


SUBSCRIPTIONS   FOR   HONE.  109 

died  just  a  year  after  the  trials  ;  but  sixty-eight  years  may  have 
had  more  to  do  with  it  than  his  defeat. 

A  large  subscription  was  raised  for  Hone,  headed  by  the  Duke 
of  Bedford  for  105Z.  Many  of  the  leading  ante-ministerialists 
joined  :  but  there  were  many  of  the  other  side  who  avowed  their 
disapprobation  of  the  false  pretence.  Many  could  not  venture 
their  names.  In  the  list  I  find :  A  member  of  the  House  of  Lords, 
an  enemy  to  persecution,  and  especially  to  religious  persecution 
employed  for  political  purposes — No  parodist,  but  an  enemy  to 
persecution — A  juryman  on  the  third  day's  trial—  Ellen  Borough 
— My  name  would  ruin  me — Oh  !  minions  of  Pitt — Oil  for  the 
Hone — The  Ghosts  of  Jeffries  and  Sir  William  Roy  [Ghosts  of 
Jeffries  in  abundance] — A  conscientious  Jury  and  a  conscientious 
Attorney,  ll.  6s.  Sd. — To  Mr.  Hone,  for  defending  in  his  own 
person  the  freedom  of  the  press,  attacked  for  a  political  object, 
under  the  old  pretence  of  supporting  Eeligion — A  cut  at  corruption 
— An  Earldom  for  myself  and  a  translation  for  my  brother — One 
who  disapproves  of  parodies,  but  abhors  persecution — From  a 
schoolboy  who  wishes  Mr.  Hone  to  have  a  very  grand  subscription 
— *  For  delicacy's  sake  forbear,'  and  '  Felix  trembled ' —  'I  will  go 
myself  to-morrow ' — Judge  Jeffries'  works  rebound  in  calf  by  Law 
— Keep  us  from  Law,  and  from  the  Shepherd's  paw — I  must  not 
give  you  my  name,  but  God  bless  you ! — As  much  like  Judge 
Jeffries  as  the  present  times  will  permit — May  Jeffries'  fame 
and  Jeffries'  fate  on  every  modern  Jeffries  wait — No  parodist, 
but  an  admirer  of  the  man  who  has  proved  the  fallacy  of  the 
Lawyer's  Law,  that  when  a  man  is  his  own  advocate  he  has  a  fool 
for  his  client — A  Mussulman  who  thinks  it  would  not  be  an  impious 
libel  to  parody  the  Koran — May  the  suspenders  of  the  Habeas 
Corpus  Act  be  speedily  suspended — Three  times  twelve  for  thrice- 
tried  Hone,  who  cleared  the  cases  himself  alone,  and  won  three 
heats  by  twelve  to  one,  \l.  16s. — A  conscientious  attorney, 
11.  6s.  Sd.— Rev.  T.  B.  Morris,  rector  of  Shelfanger,  who  dis- 
approves of  the  parodies,  but  abhors  the  making  an  affected  zeal 
for  religion  the  pretext  for  political  persecution — A  Lawyer 
opposed  in  principle  to  Law — For  the  Hone  that  set  the  razor 
that  shaved  the  rats — Rev.  Dr.  Samuel  Parr,  who  most  seriously 
disapproves  of  all  parodies  upon  the  hallowed  language  of  Scripture 
and  the  contents  of  the  Prayer-book,  but  acquits  Mr.  Hone  of 
intentional  impiety,  admires  his  talents  and  fortitude,  and 
applauds  the  good  sense  and  integrity  of  his  juries— Religion 
without  hypocrisy,  and  Law  without  partiality — 0  Law  !  0  Law  ? 
0  Law ! 


110  A   BUDGET  OF  PARADOXES. 

These  are  specimens  of  a  great  many  allusive  mottoes.  The 
subscription  was  very  large,  and  would  have  bought  a  handsome 
annuity,  but  Hone  employed  it  in  the  bookselling  trade,  and  did 
not  thrive.  His  '  Everyday  Book '  and  his  '  Apocryphal  New 
Testament '  are  useful  books.  On  an  annuity  he  would  have 
thriven  as  an  antiquarian  writer  and  collector.  It  is  well  that 
the  attack  upon  the  right  to  ridicule  Ministers  roused  a  dormant 
power  which  was  equal  to  the  occasion.  Hone  declared,  on  his 
honour,  that  he  had  never  addressed  a  meeting  in  his  life,  nor 
spoken  a  word  before  more  than  twelve  persons.  Had  he — which 
however  could  not  then  be  done — employed  counsel,  and  had  a 
guilty  defence  made  for  him,  he  would  very  likely  have  been 
convicted,  and  the  work  would  have  been  left  to  be  done  by 
another.  No  question  that  the  parodies  disgusted  all  who 
reverenced  Christianity,  and  who  could  not  separate  the  serious  and 
the  ludicrous,  and  prevent  their  existence  in  combination. 

My  extracts,  &c.,  are  from  the  nineteenth,  seventeenth,  and  six- 
teenth editions  of  the  three  trials,  which  seem  to  have  been  con- 
temporaneous (all  in  1818)  as  they  are  made  up  into  one  book, 
with  additional  title  over  all,  and  the  motto  '  Thrice  the  brindled 
cat  hath  mew'd.'  They  are  published  by  Hone  himself,  who  I 
should  -have  said  was  a  publisher  as  well  as  was  to  be.  And 
though  the  trials  only  ended  Dec.  20,  1817,  the  preface  attached 
to  this  common  title  is  dated  Jan.  23,  1818. 

The  spirit  which  was  roused  against  the  false  dealing  of 
the  Government,  i.e.  the  pretence  of  prosecuting  for  impiety 
when  all  the  world  knew  the  real  offence  was,  if  anything,  sedi- 
tion— was  not  got  up  at  the  moment :  there  had  been  previous 
exhibitions  of  it.  For  example,  in  the  spring  of  1 8 1 8  Mr.  Russell, 
a  little  printer  in  Birmingham,  was  indicted  for  publishing  the 
Political  Litany  on  which  Hone  was  afterwards  tried.  He  took 
his  witnesses  to  the  summer  Warwick  assizes,  and  was  told  that 
the  indictment  had  been  removed  by  certiorari  into  the  King's 
Bench.  He  had  notice  of  trial  for  the  spring  assizes  at  Warwick: 
he  took  his  witnesses  there,  and  the  trial  was  postponed  by  the 
Crown.  He  then  had  notice  for  the  summer  assizes  at  Warwick  ; 
and  so  on.  The  policy  seems  to  have  been  to  wear  out  the  ob- 
noxious parties,  either  by  delays  or  by  heaping  on  trials.  The 
Government  was  odious,  and  knew  it  could  not  get  verdicts  against 
ridicule,  and  could  get  verdicts  against  impiety.  No  difficulty 
was  found  in  convicting  the  sellers  of  Paine's  works,  and  the  like. 
When  Hone  was  held  to  bail  it  was  seen  that  a  crisis  was  at  hand. 
All  parties  in  politics  furnished  him  with  parodies  in  proof  of 


PROFANITY  OF  LORD  BYROX.  Ill 

religious  persons  having  made  instruments  of  them.  The  parodies 
by  Addison  and  Luther  were  contributed  by  a  Tory  lawyer,  who 
was  afterwards  a  judge. 

Hone  had  published,  in  1817,  tracts  of  purely  political  ridicule: 
'  official  account  of  the  noble  lord's  bite,'  *  trial  of  the  dog  for 
biting  the  noble  lord,'  &c.  These  were  not  touched.  After  the 

o  7 

trials,  it  is  manifest  that  Hone  was  to  be  unassailed,  do  what  he 
might.  '  The  Political  House  that  Jack  built,'  in  1 8 1 9  ;  «  The  Man 
in  the  Moon,'  1 820  ;  '  The  Queen's  Matrimonial  Ladder,'  '  Non  mi 
ricordo,'  'The  E— 1  fowls,'  1 820  ;  '  The  Political  Showman  at  home,' 
with  plates  by  G.  Cruickshank,  1821  [he  did  all  the  plates]  ;  '  The 
Spirit  of  Despotism,'  1821 — would  have  been  legitimate  marks 
for  prosecution  in  previous  years.  The  biting  caricature  of 
several  of  these  works  are  remembered  to  this  day.  '  The  Spirit 
of  Despotism'  was  a  tract  of  1795,  of  which  a  few  copies  had  been 
privately  circulated  with  great  secrecy.  Hone  reprinted  it,  and 
prefixed  the  following  address  to  '  Robert  Stewart,  alias  Lord 
Castlereagh ' — '  It  appears  to  me  that  if,  unhappily,  your  counsels 
are  allowed  much  longer  to  prevail  in  the  Brunswick  Cabinet, 
they  will  bring  on  a  crisis,  in  which  the  king  may  be  dethroned 
or  the  people  enslaved.  Experience  has  shown  that  the  people 
will  not  l>e  enslaved — the  alternative  is  the  affair  of  your  em- 
ployers.' Hone  might  say  this  without  notice. 

In  1819  Mr.  Murray  published  Lord  Byron's  'Don  Juan,'  and 
Hone  followed  it  with  '  Don  John,  or  Don  Juan  unmasked,'  a 
little  account  of  what  the  publisher  to  the  Admiralty  was  allowed 
to  issue  without  prosecution.  The  parody  on  the  Commandments 
was  a  case  very  much  in  point :  and  Hone  makes  a  stinging 
allusion  to  the  use  of  the  '  unutterable  Nvme,  with  a  profane 
levity  unsurpassed  by  any  other  two  lines  in  the  English  language.* 
The  lines  are 

'Tis  strange — the  Hebrew  noun  which  means  'I  am,' 
The  English  always  use  to  govern  d n. 

Hone  ends  with  : '  Lord  Byron's  dedication  of  "  Don  Juan  "  to  Lord 
Castlereagh  was  suppressed  by  Mr.  Murray  from  delicacy  to 
Ministers.  Q.  Why  did  not  Mr.  Murray  suppress  Lord  Byron's 
parody  on  the  Ten  Commandments?  A.  Because  it  contains 
nothing  in  ridicule  of  Ministers,  and  therefore  nothing  that  they 
could  suppose  would  lead  to  the  displeasure  of  Almighty  God.' 

The  little  matters  on  which  I  have  dwelt  will  never  appear  in 
history  from  their  political  importance,  except  in  a  few  words  of 
result.  As  a  mode  of  thought,  silly  evasions  of  all  kinds  belong 


112  A  BUDGET   OF   PARADOXES. 

to  such  a  work  as  the  present.  Ignorance,  which  seats  itself  in 
the  chair  of  knowledge,  is  a  mother  of  revolutions  in  politics,  and 
of  unread  pamphlets  in  circle-squaring.  From  1815  to  1830  the 
question  of  revolution  or  no  revolution  lurked  in  all  our  English 
discussions.  The  high  classes  must  govern ;  the  high  classes 
shall  not  govern  ;  and  thereupon  issue  was  to  be  joined.  In  1828- 
1833  the  question  came  to  issue;  and  it  was,  Eevolution  with  or 
without  civil  war ;  choose.  The  choice  was  wisely  made  ;  and 
the  Eeform  Bill  started  a  new  system  so  well  dovetailed  into  the 
old  that  the  joinings  are  hardly  visible.  And  now,  in  1867,  the 
thing  is  repeated  with  a  marked  subsidence  of  symptoms  ;  and  the 
party  which  has  taken  the  place  of  the  extinct  Tories  is  carrying 
through  Parliament  a  wider  extension  of  the  franchise  than  their 
opponents  would  have  ventured.  Napoleon  used  to  say  that  a 
decided  nose  was  a  sign  of  power :  on  which  it  has  been  remarked 
that  he  had  good  reason  to  say  so  before  the  play  was  done.  And 
so  had  our  country ;  it  was  saved  from  a  religious  war,  and  from 
a  civil  war,  by  the  power  of  that  nose  over  its  colleagues. 

The    Commentaries  of  Proclus.      Translated  by  Thomas  Taylor. 
London,  1792,  2  vols.  4to. 

The  reputation  of  '  the  Platonist '  begins  to  grow,  and  will 
continue  to  grow.  The  most  authentic  account  is  in  the  Penny 
Cyclopaedia,  written  by  one  of  the  few  persons  who  knew  him 
well,  and  one  of  the  fewer  who  possess  all  his  works.  At  page 
Ivi.  of  the  Introduction  is  Taylor's  notion  of  the  way  to  find  the 
circumference.  It  is  not  geometrical,  for  it  proceeds  on  the 
motion  of  a  point:  'the  words  '  on  account  of  the  simplicity  of  the 
impulsive  motion,  such  a  line  must  be  either  straight  or  circular' 
will  suffice  to  show  how  Platonic  it  is.  Taylor  certainly  professed 
a  kind  of  heathenism.  D'Israeli  said,  'Mr.  T.  Taylor,  the  Platonic 
philosopher  and  the  modern  Plethon,  consonant  to  that  philosophy, 
professes  polytheism.'  Taylor  printed  this  in  large  type,  in  a 
page  by  itself  after  the  dedication,  without  any  disavowal.  I 
have  seen  the  following,  Greek  and  translation  both,  in  his  hand- 
writing : — '  Has  dyaQos  rj  dyaSos  sQviKOs'  Kai  iras  ^pia-navos  y 
"XpicfTtavos  KaKus.  Every  good  man,  so  far  as  he  is  a  good  man, 
is  a  heathen  ;  and  every  Christian,  so  far  as  he  is  a  Christian,  is  a 
bad  man.'  Whether  Taylor  had  in  his  head  the  Christian  of  the 
New  Testament,  or  whether  he  drew  from  those  members  of  the 
'  religious  world '  who  make  manifest  the  religious  flesh  and  the 
religious  devil,  cannot  be  decided  by  us,  and  perhaps  was  not 
known  to  himself.  If  a  heathen,  he  was  a  virtuous  one. 


HANNAH  MORE -MISS  BURNEY.  113 

(1795.)  This  is  the  date  of  a  very  remarkable  paradox.  The 
religious  world — to  use  a  name  claimed  by  a  doctrinal  sect — 
had  long  set  its  face  against  amusing  literature,  and  all  works  of 
imagination.  Bunyan,  Milton,  and  a  few  others  were  irresis- 
tible ;  but  a  long  face  was  pulled  at  every  attempt  to  produce 
something  readable  for  poor  people  and  poor  children.  In 
1795,  a  benevolent  association  began  to  circulate  the  works  of 
a  lady  who  had  been  herself  a  dramatist,  and  had  nourished  a 
pleasant  vein  of  satire  in  the  society  of  Garrick  and  his  friends  ; 
all  which  is  carefully  suppressed  in  some  biographies.  Hannah 
More's  Cheap  Repository  Tracts,  which  were  bought  by  millions 
of  copies,  destroyed  the  vicious  publications  with  which  the 
hawkers  deluged  the  country,  by  the  simple  process  of  furnishing 
the  hawkers  with  something  more  saleable. 

Dramatic  fiction,  in  which  the  characters  are  drawn  by  them- 
selves, was,  at  the  middle  of  the  last  century,  the  monopoly  of 
writers  who  required  indecorum,  such  as  Fielding  and  Smollett. 
All,  or  nearly  all,  which  could  be  permitted  to  the  young,  was 
dry  narrative,  written  by  people  who  could  not  make  their 
personages  talk  character ;  they  all  spoke  alike.  The  author 
of  the  Rambler  is  ridiculed,  because  his  young  ladies  talk 
Johnsonese  ;  but  the  satirists  forget  that  all  the  presentable  novel- 
writers  were  equally  incompetent ;  even  the  author  of  '  Zeluco  ' 
(1789)  is  the  strongest  possible  case  in  point. 

Dr.  Moore,  the  father  of  the  hero  of  Corunna,  with  good  narra- 
tive power,  some  sly  humour,  and  much  observation  of  character, 
would  have  been,  in  our  day,  a  writer  of  the  Peacock  family. 
Nevertheless,  to  one  who  is  accustomed  to  our  style  of  things, 
it  is  comic  to  read  the  dialogue  of  a  jealous  husband,  a  suspected 
wife,  a  faithless  maid-servant,  a  tool  of  a  nurse,  a  wrong-headed 
pomposity  of  a  priest,  and  a  sensible  physician,  all  talking  Dr. 
Moore  through  their  masks.  Certainly  an  Irish  soldier  does  say 
by  Jasus,  and  a  cockney  footman  this  here  and  that  there ;  and 
this  and  the  like  is  all  the  painting  of  characters  which  is  effected 
out  of  the  mouths  of  the  bearers  by  a  narrator  of  great  power. 
I  suspect  that  some  novelists  repressed  their  power  under  a  rule 
that  a  narrative  should  narrate,  and  that  the  dramatic  should  be 
confined  to  the  drama. 

I  make  no  exception  in  favour  of  Miss  Burney ;  though  she  was 
the  forerunner  of  a  new  era.  Suppose  a  country  in  which  dress 
is  always  of  one  colour  ;  suppose  an  importer  who  brings  in  cargoes 
of  blue  stuff,  red  stuff,  green  stuff,  &c.,  and  exhibits  dresses  of 
these  several  colours,  that  person  is  the  similitude  of  Miss 

i 


114  A   BUDGET   OF  PAKADOXES. 

Burney.  It  would  be  a  delightful  change  from  a  universal  dull 
brown,  to  see  one  person  all  red,  another  all  blue,  &c. ;  but  the 
•  real  inventor  of  pleasant  dress  would  be  the  one  who  could  mix 
his  colours  and  keep  down  the  bright  and  gaudy.  Miss  Burney's 
introduction  was  so  charming,  by  contrast,  that  she  nailed  such  men 
as  Johnson,  Burke,  Grarrick,  &c.,  to  her  books.  But  when  a 
person  who  has  read  them  with  keen  pleasure  in  boyhood,  as  I 
did,  comes  back  to  them  after  a  long  period,  during  which  he 
has  made  acquaintance  with  the  great  novelists  of  our  century, 
three-quarters  of  the  pleasure  is  replaced  by  wonder  that  he  had 
not  seen  he  was  at  a  puppet-show,  not  at  a  drama.  Take  some 
labelled  characters  out  of  our  humourists,  let  them  be  put 
together  into  one  piece,  to  speak  only  as  labelled  :  let  there  be 
a  Dominie  with  nothing  but  'Prodigious  ! '  a  Dick  Swiveller  with 
nothing  but  adapted  quotations  ;  a  Dr.  Folliott  with  nothing 
but  sneers  at  Lord  Brougham  ;  and  the  whole  will  pack  up  into 
one  of  Miss  Burney's  novels. 

Maria  Edgeworth,  Sydney  Owenson  (Lady  Morgan),  Jane 
Austen,  Walter  Scott,  &c.,  are  all  of  our  century ;  as  are,  I 
believe,  all  the  Minerva  Press  novels,  as  they  were  called,  which 
show  some  of  the  power  in  question.  Perhaps  dramatic  talent 
found  its  best  encouragement  in  the  drama  itself.  But  I  cannot 
ascertain  that  any  such  power  was  directed  at  the  multitude, 
whether  educated  or  uneducated,  with  natural  mixture  of 
character,  under  the  restraints  of  decorum,  until  the  use  of  it 
by  two  religious  writers  of  the  school  called  '  evangelical,'  Han- 
nah More  and  Rowland  Hill.  The  Village  Dialogues,  though 
not  equal  to  the  Repository  Tracts,  are  in  many  parts  an  ap- 
proach, and  perhaps  a  copy ;  there  is  frequently  humorous  satire, 
in  that  most  effective  form,  self-display.  They  were  published  in 
1800,  and,  partly  at  least,  by  the  Religious  Tract  Society,  the 
lineal  successor  of  the  Repository  association,  though  knowing 
nothing  about  its  predecessor.  I  think  it  right  to  add  that 
Rowland  Hill  here  mentioned  is  not  the  regenerator  of  the 
Post  Office.  Some  do  not  distinguish  accurately  ;  I  have  heard 
of  more  than  one  who  took  me  to  have  had  a  logical  controversy 
with  a  diplomatist  who  died  some  years  before  I  was  born. 

A  few  years  ago,  an  attempt  was  made  by  myself  and  others 
to  collect  some  information  about  the  Cheap  Repository  (see 
Notes  and  Queries,  3rd  Series,  vi.  241,  290,  353 ;  Christian 
Observer,  Dec.  1864,  pp.  944-49).  It  appeared  that  after  the 
Religious  Tract  Society  had  existed  more  than  fifty  years,  a  friend 
presented  it  with  a  copy  of  the  original  prospectus  of  the  Rcposi- 


THE   EELIGIOUS   TEACT   SOCIETY.  115 

tory,  a  thing  the  existence  of  which  was  not  known.  In  this 
prospectus  it  is  announced  that  from  the  plan  '  will  be  carefully 
excluded  whatever  is  enthusiastic,  absurd,  or  superstitious.'  The 
*  evangelical '  party  had,  from  the  foundation  of  the  Eeligious 
Tract  Society,  regretted  that  the  Repository  Tracts  '  did  not 
contain  a  fuller  statement  of  the  great  evangelical  principles ;' 
while  in  the  prospectus  it  is  also  stated  that  '  no  cause  of  any 
particular  party  is  intended  to  be  served  by  it,  but  general 
Christianity  will  be  promoted  upon  practical  principles.'  This 
explains  what  has  often  been  noticed,  that  the  tracts  contain  a 
mild  form  of  the  '  evangelical '  doctrine,  free  from  that  more 
fervid  dogmitism  which  appears  in  the  Village  Dialogues;  and 
such  as  H.  More's  friend,  Bishop  Porteus — a  great  promoter  of 
the  scheme — might  approve.  The  Religious  Tract  Society  (in 
1863)  republished  some  of  H.  More's  tracts,  with  alterations, 
additions,  and  omissions  ad  libitum.  This  is  an  improper  way 
of  dealing  with  the  works  of  the  dead  ;  especially  when  the 
reprints  are  of  popular  works.  A  small  type  addition  to  the 
preface  contains :  '  Some  alterations  and  abridgments  have  been 
made  to  adapt  them  to  the  present  times  and  the  aim  of  the 
Religious  Tract  Society.'  I  think  every  publicity  ought  to  be 
given  to  the  existence  of  such  a  practice ;  and  I  reprint  what  I 
said  on  the  subject  in  Notes  and  Queries. 

Alterations  in  works  which  the  Society  republishes  are  a  neces- 
sary part  of  their  plan,  though  such  notes  as  they  should  judge 
to  be  corrective  would  be  the  best  way  of  proceeding.  But  the 
fact  of  alteration  should  be  very  distinctly  announced  on  the  title 
of  the  work  itself,  not  left  to  a  little  bit  of  small  type  at  the  end 
of  the  preface,  in  the  place  where  trade  advertisements,  or  direc- 
tions to  the  binder,  are  often  found.  And  the  places  in  which 
alteration  has  been  made  should  be  pointed  out,  either  by  marks 
of  omission,  when  omission  is  the  alteration,  or  by  putting  the 
altered  sentences  in  brackets,  when  change  has  been  made.  May 
any  one  alter  the  works  of  the  dead  at  his  own  discretion  ?  We 
all  know  that  readers  in  general  will  take  each  sentence  to  be 
that  of  the  author  whose  name  is  on  the  title;  so  that  a  correcting 
republisher  makes  use  of  his  author's  n-ame  to  teach  his  own 
variation.  The  tortuous  logic  of  '  the  trade,'  which  is  content 
when  '  the  world '  is  satisfied,  is  not  easily  answered,  any  more 
than  an  eel  is  easily  caught ;  but  the  Religious  Tract  Society  may 
be  convinced  [in  the  old  sense]  in  a  sentence.  On  which  course 
would  they  feel  most  safe  in  giving  their  account  to  the  God  of 
truth  ?  '  In  your  own  conscience,  now  ? ' 

i  -2 


116  A  BUDGET  OF  PAEADOXES. 

I  have  tracked  out  a  good  many  of  the  variations  made  by  the 
Religious  Tract  Society  in  the  recently  published  volume  of 
Repository  Tracts.  Most  of  them  are  doctrinal  insertions  or 
amplifications,  to  the  matter  of  which  Hannah  More  would  not 
have  objected — all  that  can  be  brought  against  them  is  the  want 
of  notice.  But  I  have  found  two  which  the  respect  I  have  for  the 
Religious  Tract  Society,  in  spite  of  much  difference  on  various 
points,  must  not  prevent  my  designating  as  paltry.  In  the  story 
of  Mary  Wood,  a  kind-hearted  clergyman  converses  with  the  poor 
girl  who  has  ruined  herself  by  lying.  In  the  original,  he  '  assisted 
her  in  the  great  work  of  repentance  ; '  in  the  reprint  it  is  to  be 
shown  in  some  detail  how  he  did  this.  He  is  to  begin  by  pointing 
out  that  '  the  heart  is  deceitful  above  all  things  and  desperately 
wicked.'  Now  the  clergyman's  name  is  Heartwell :  so  to  prevent 
his  name  from  contradicting  his  doctrine,  he  is  actually  cut  down 
to  Harwell.  Hannah  More  meant  this  good  man  for  one  of  those 
described  in  Acts  xv.  8,  9,  and  his  name  was  appropriate. 

Again,  Mr.  Flatterwell,  in  persuasion  of  Parley  the  porter  to 
let  him  into  the  castle,  declares  that  the  worst  he  will  do  is  to 
'  play  an  innocent  game  of  cards  just  to  keep  you  awake,  or  sing 
a  cheerful  song  with  the  maids.'  Oh  fie  !  Miss  Hannah  More  ! 
and  you  a  single  lady  too,  and  a  contemporary  of  the  virtuous 
Bowdler  !  Though  Flatterwell  be  an  allegory  of  the  devil,  this 
is  really  too  indecorous,  even  for  him.  Out  with  the  three  last 
words !  and  out  it  is. 

The  Society  cuts  a  poor  figure  before  a  literary  tribunal. 
Nothing  was  wanted  except  an  admission  that  the  remarks  made  by 
me  were  unanswerable,  and  this  was  immediately  furnished  by  the 
Secretary  (N.  and  Q.  3  S.  vi.  290).  In  a  reply  of  which  six  parts 
out  of  seven  are  a  very  amplified  statement  that  the  Society  did 
not  intend  to  reprint  all  Hannah  More's  tracts,  the  remaining 
seventh  is  as  follows  : — 

I  am  not  careful  [perhaps  this  should  be  careful  not~]  to  notice 
Professor  De  Morgan's  objections  to  the  changes  in  'Mary  Wood'  or 
*  Parley  the  Porter,'  but  would  merely  reiterate  that  the  tracts  were 
neither  designed  nor  announced  to  be  '  reprints '  of  the  originals 
[design  is  only  known  to  the  designers  ;  as  to  announcement,  the  title  is 
1  'Tis  all  for  the  best,  The  Shepherd  of  Salisbury  Plain,  and  other 
narratives,  by  Mrs.  Hannah  More ']  ;  and  much  less  [this  must  be 
careful  not;  further  removed  from  answer  than  not  careful']  can  I 
oncupy  your  space  by  a  treatise  on  the  Professor's  question :  '  May 
any  one  alter  the  works  of  the  dead  at  his  own  discretion  ? ' 

To  which  I  say — Thanks  for  help  ! 


WILLIAM   FREND'S   ALGEBRA.  117 

I  predict  that  Hannah  More's  Cheap  Repository  Tracts  will 
somewhat  resemble  the  Pilgrim's  Progress  in  their  fate.  Written 
for  the  cottage,  and  long  remaining  in  their  original  position, 
they  will  become  classical  works  of  their  kind.  Most  assuredly 
this  will  happen  if  my  assertion  cannot  be  upset,  namely — That 
they  contain  the  first  specimens  of  fiction  addressed  to  the  world 
at  large,  and  widely  circulated,  in  which  dramatic — as  distin- 
guished from  puppet — power  is  shown,  and  without  indecorum. 

According  to  some  statements  I  have  seen,  but  which  I  have 
not  verified,  other  publishing  bodies,  such  as  the  Christian 
Knowledge  Society,  have  taken  the  same  liberty  with  the  names 
of  the  dead  as  the  Eeligious  Tract  Society.  If  it  be  so,  the 
impropriety  is  the  work  of  the  smaller  spirits,  who  have  not  been 
sufficiently  overlooked.  There  must  be  an  overwhelming  majority 
in  the  higher  councils  to  feel  that,  whenever  altered  works  are 
published,  the  fact  of  alteration  should  be  made  as  prominent  as 
the  name  of  the  author.  Everything  short  of  this  is  suppression 
of  truth,  and  will  ultimately  destroy  the  credit  of  the  Society. 
Equally  necessary  is  it  that  the  alterations  should  be  noted. 
When  it  comes  to  be  known  that  the  author  before  him  is  altered, 
he  knows  not  where  nor  how  nor  by  whom,  the  lowest  reader  will 
lose  his  interest. 


The  principles  of  Algebra.     By  William  Frend.     London,  1796, 
8vo.     Second  Part,  1799. 

This  Algebra,  says  Dr.  Peacock,  shows  '  great  distrust  of  the 
results  of  algebraical  science  which  were  in  existence  at  the  time 
when  it  was  written.'  Truly  it  does ;  for,  as  Dr.  Peacock  had 
shown  by  full  citation,  it  makes  war  of  extermination  upon  all 
that  distinguishes  algebra  from  arithmetic.  Robert  Simson  and 
Baron  Maseres  were  Mr.  Frend's  predecessors  in  this  opinion. 

The  genuine  respect  which  I  entertained  for  my  father-in-law 
did  not  prevent  my  canvassing  with  perfect  freedom  his  anti- 
algebraical  and  anti-Newtonian  opinions,  in  a  long  obituary 
memoir  read  at  the  Astronomical  Society  in  February  1842, 
which  was  written  by  me.  It  was  copied  into  the  Athenceum  of 
March  19.  It  must  be  said  that  if  the  manner  in  which  algebra 
was  presented  to  the  learner  had  been  true  algebra,  he  would 
have  been  right :  and  if  he  had  confined  himself  to  protesting 
against  the  imposition  of  attraction  as  a  fundamental  part  of  the 
existence  of  matter,  he  would  have  been  in  unity  with  a  great 
many,  including  Newton  himself.  I  wish  he  had  preferred 


113  A   BUDGET   OF   PARADOXES. 

amendment  to  rejection  when  he  was  a  college   tutor  :  he  wrote 
and  spoke  English  with  a  clearness  which  is  seldom  equalled. 

His  anti-Newtonian  discussions  are  confined  to  the  preliminary 
chapters  of  his  *  Evening  Amusements,'  a  series  of  astronomical 
lessons  in  nineteen  volumes,  following  the  moon  through  a  period 
of  the  golden  numbers. 

There  is  a  mistake  about  him  which  can  never  be  destroyed. 
It  is  constantly  said  that,  at  his  celebrated  trial  in  1792,  for 
sedition  and  opposition  to  the  Liturgy,  &c.,  he  was  expelled  the 
University.  He  was  banished.  People  cannot  see  the  difference; 
but  it  made  all  the  difference  to  Mr.  Frend.  He  held  his  fellow- 
ship and  its  profits  till  his  marriage  in  1808,  and  was  a  member 
of  the  University  and  of  its  Senate  till  his  death  in  1841,  as  any 
Cambridge  Calendar  up  to  1841  will  show.  That  they  would  have 
expelled  him  if  they  could,  is  perfectly  true  ;  and  there  is  a  funny 
story — also  perfectly  true — about  their  first  proceedings  being 
under  a  statute  which  would  have  given  the  power,  had  it  not  been 
discovered  during  the  proceedings  that  the  statute  did  not  exist. 
It  had  come  so  near  to  existence  as  to  be  entered  into  the  Vice- 
Chancellor's  book  for  his  signature,  which  it  wanted,  as  was  not 
seen  till  Mr.  Frend  exposed  it :  in  fact,  the  statute  had  never 
actually  passed. 

There  is  an  absurd  mistake  in  Gunning's  '  Reminiscences  of 
Cambridge.'  In  quoting  a  passage  of  Mr.  Frend's  pamphlet, 
which  was  very  obnoxious  to  the  existing  Government,  it  is 
printed  that  the  poor  market-women  complained  that  they  were 
to  be  scotched  a  quarter  of  their  wages  by  taxation ;  and  attention 
is  called  to  the  word  by  its  being  three  times  printed  in  italics. 
In  the  pamphlet  it  is  '  sconced  ' ;  that  very  common  old  word  for 
fined  or  mulcted. 

Lord  Lyndhurst,  who  has  [1863]  just  passed  away  under  a  load 
of  years  and  honours,  was  Mr.  Frend's  private  pupil  at  Cambridge. 
At  the  time  of  the  celebrated  trial,  he  and  two  others  amused 
themselves,  and  vented  the  feeling  which  was  very  strong  among 
the  undergraduates,  by  chalking  the  walls  of  Cambridge  with 
'  Frend  for  ever!'  While  thus  engaged  in  what,  using  the  term 
legally,  we  are  probably  to  call  his  first  publication,  he  and  his 
friends  were  surprised  by  the  proctors.  Flight  and  chase  followed 
of  course:  Copley  and  one  of  the  others,  Serjeant  Rough, 
escaped  ;  the  third,  whose  name  I  forget,  but  who  afterwards,  I 
have  been  told,  was  a  bishop,1  being  lame,  was  captured  and 
impositioned.  Looking  at  the  Cambridge  Calendar  to  verify  the 

1  Herbert  Marsh,  afterwards  Bishop  of  Peterborough,  a  relation  of  my  father,  (Ed.) 


FRANCIS   PLACE— WILLIAM   COBBETT.  119 

fact  that  Copley  was  an  undergraduate  at  the  time,  I  find  that 
there  are  but  two  other  men  in  the  list  of  honours  of  his  year 
whose  names  are  now  widely  remembered.  And  they  were  both 
celebrated  schoolmasters  ;  Butler  of  Harrow,  and  Tate  of  Eichmond. 

But  Mr.  Frend  had  another  noted  pupil.  I  once  had  a  con- 
versation with  a  very  remarkable  man,  who  was  generally  called 
'  Place,  the  tailor,'  but  who  was  politician,  political  economist, 
&c.,  &c.  He  sat  in  the  room  above  his  shop — he  was  then  a 
thriving  master  tailor  at  Charing  Cross — surrounded  by  books 
enough  for  nine,  to  shame  a  proverb.  The  blue  books  alone,  cut 
up  into  strips,  would  have  measured  Great  Britain  for  oh-no-we- 
never-mention-'ems,  the  Highlands  included.  I  cannot  find  a 
biography  of  this  worthy  and  able  man.  I  happened  to  mention 
William  Frend,  and  he  said,  '  Ah !  my  old  master,  as  I  always 
call  him.  Many  and  many  a  time,  and  year  after  year,  did  he 
come  in  every  now  and  then  to  give  me  instruction,  while  I  was 
sitting  on  the  board,  working  for  my  living,  you  know.' 

Place,  who  really  was  a  sound  economist,  is  joined  with 
Cobbett,  because  they  were  together  at  one  time,  and  because  he 
was,  in  1800,  &c.,  a  great  Eadical.  But  for  Cobbett  he  had  a 
great  contempt.  He  told  me  the  following  story.  He  and  others 
were  advising  with  Cobbett  about  the  defence  he  was  to  make  on 
a  trial  for  seditious  libel  which  was  coming  on.  Said  Place,  *  You 
must  put  in  the  letters  you  have  received  from  Ministers, 
members  of  the  Commons  from  the  Speaker  downwards,  &c., 
about  your  Eegister,  and  their  wish  to  have  subjects  noted.  You 
must  then  ask  the  jury  whether  a  person  so  addressed  must  be 
considered  as  a  common  sower  of  sedition,  &c.  You  will  be 
acquitted ;  nay,  if  your  intention  should  get  about,  veiy  likely 
they  will  manage  to  stop  proceedings.'  Cobbett  was  too  much 

disturbed  to  listen  ;  he  walked  about  the  room  ejaculating  '  D 

the  prison  ! '  and  the  like.  He  had  not  the  sense  to  follow  the 
advice,  and  was  convicted. 

Cobbett,  to  go  on  with  the  chain,  was  a  political  acrobat,  ready 
for  any  kind  of  posture.  A  friend  of  mine  gave  me  several  times 
an  account  of  a  mission  to  him.  A  Tory  member — those  who 
know  the  old  Tory  world  may  look  for  his  initials  in  initials  of 
two  consecutive  words  of  '  Pay  his  money  with  interest ' — who 
was,  of  course,  a  political  opponent,  thought  Cobbett  had  been 
hardly  used,  and  determined  to  subscribe  handsomely  towards  the 
expenses  he  was  incurring  as  a  candidate.  My  friend  was  com- 
missioned to  hand  over  the  money — a  bag  of  sovereigns,  that  notes 
might  not  be  traced.  He  went  into  Cobbett's  committee-room, 


120  A   BUDGET   OF  PARADOXES. 

told  the  patriot  his  errand,  and  put  the  money  on  the  table. 
'  And  to  whom,  sir,  am  I  indebted  ? '  said  Cobbett.  '  The  donor,' 
was  the  answer,  '  is  Mr.  Andrew  Theophilus  Smith,'  or  some  such 
unlikely  pair  of  baptismals.  '  Ah ! '  said  Cobbett,  '  I  have  known  Mr. 
A.  T.  S.  a  long  time !  he  was  always  a  true  friend  of  his  country  1 ' 
To  return  to  Place.  He  is  a  noted  instance  of  the  advantage 
of  our  jury  system,  which  never  asks  a  man's  politics,  &c.  The 
late  King  of  Hanover,  when  Duke  of  Cumberland,  being  unpopular, 
was  brought  under  unjust  suspicions  by  the  suicide  of  his  valet : 
he  must  have  seduced  the  wife  and  murdered  the  husband.  The 
charges  were  as  absurd  as  those  brought  against  the  Englishman 
in  the  Frenchman's  attempt  at  satirical  verses  upon  him  : — 

The  Englishman  is  a  very  bad  man  ; 
He  drink  the  beer  and  lie  steal  the  can  : 
He  kiss  the  wife  and  he  beat  the  man  ; 
And  the  Englishman  is  a  very  G d . 


The  charges  were  revived  in  a  much  later  day,  and  the  defence 
might  have  given  some  trouble.  But  Place,  who  had  been  the 
foreman  at  the  inquest,  came  forward,  and  settled  the  question  in 
a  few  lines.  Everyone  knew  that  the  old  Radical  was  quite  free 
of  all  disposition  to  suppress  truth  from  wish  to  curry  favour  with 
royalty. 

John  Speed,  the  author  of  the  English  History  (1632)  which 
Bishop  Nicolson  calls  the  best  chronicle  extant,  was  a  man,  like 
Place,  of  no  education  but  what  he  gave  himself.  The  bishop 
says  he  would  have  done  better  if  he  had  had  better  training : 
but  what,  he  adds,  could  have  been  expected  from  a  tailor  !  This 
Speed  was,  as  well  as  Place.  But  he  was  released  from  manual 
labour  by  Sir  Fulk  Grevil,  who  enabled  him  to  study. 

I  have  elsewhere  noticed  that  those  who  oppose  the  mysteries 
of  algebra  do  not  ridicule  them ;  this  I  want  the  cyclometers  to 
do.  Of  the  three  who  wrote  against  the  great  point,  the  negative 
quantity,  and  the  uses  of  0  which  are  connected  with  it,  only 
one  could  fire  a  squib.  That  Robert  Simson  should  do  such  a 
thing  will  be  judged  impossible  by  all  who  admit  tradition.  I 
do  not  vouch  for  the  following  ;  I  give  it  as  a  proof  of  the 
impression  which  prevailed  about  him : — 

He  used  to  sit  at  his  open  window  on  the  ground  floor,  as  deep 
in  geometry  as  a  Robert  Simson  ought  to  be.  Here  he  would  be 
accosted  by  beggars,  to  whom  he  generally  gave  a  trifle ,  he 
roused  himself  to  hear  a  few  words  of  the  story,  made  his  dona- 
tion, and  instantly  dropped  down  into  his  depths.  Some  wags 


MASERES   ON   THE   NEGATIVE   SIGN.  121 

one  day  stopped  a  mendicant  who  was  on  his  way  to  the  window, 
with  '  Now,  my  man,  do  as  we  tell  you,  and  you  will  get  some- 
thing from  that  gentleman,  and  a  shilling  from  us  besides.  You 
will  go  and  say  you  are  in  distress,  he  will  ask  you  who  you  are, 
and  you  will  say  you  are  Robert  Simson,  son  of  John  Simson  of 
Kirktonhill.'  The  man  did  as  he  was  told  ;  Simson  quietly  gave 
him  a  coin,  and  dropped  off.  The  wags  watched  a  little,  and  saw 
him  rouse  himself  again,  and  exclaim  '  Robert  Simson,  son  of 
John  Simson  of  Kirktonhill !  why,  that  is  myself.  That  man 
must  be  an  impostor.'  Lord  Brougham  tells  the  same  story,  with 
some  difference  of  details. 

Baron  Maseres  was,  as  a  writer,  dry ;  those  who  know  his 
writings  will  feel  that  he  seldom  could  have  taken  in  a  joke  or 
issued  a  pun.  Maseres  was  the  fourth  wrangler  of  1752,  and 
first  Chancellor's  medallist  (or  highest  in  classics) ;  his  second 
was  Porteus  (afterwards  Bishop  of  London).  Waring  came  five 
years  after  him :  he  could  not  get  Maseres  through  the  second 
page  of  his  first  work  on  algebra ;  a  negative  quantity  stood 
like  a  lion  in  the  way.  In  1758  he  published  his 'Dissertation 
on  the  Use  of  the  Negative  Sign,'  4to.  There  are  some  who  care 
little  about  -f-  and  — ,  who  would  give  it  house-room  for  the  sake 
of  the  four  words  '  Printed  by  Samuel  Richardson.' 

Maseres  speaks  as  follows :  '  A  single  quantity  can  never  be 
marked  with  either  of  those  signs,  or  considered  as  either  affirma- 
tive or  negative ;  for  if  any  single  quantity,  as  6,  is  marked 
either  with  the  sign  -f-  or  with  the  sign  —  without  assigning 
some  other  quantity,  as  a,  to  which  it  is  to  be  added,  or  from 
which  it  is  to  be  subtracted,  the  mark  will  have  no  meaning  or 
signification :  thus  if  it  be  said  that  the  square  of  —  5,  or  the 
product  of  — 5  into  —5,  is  equal  to  +25,  such  an  assertion  must 
either  signify  no  more  than  that  5  times  5  is  equal  to  25  without 
any  regard  to  the  signs,  or  it  must  be  mere  nonsense  and  unin- 
telligible jargon.  I  speak  according  to  the  foregoing  definition, 
by  which  the  affirmativeness  or  negativeness  of  any  quantity 
implies  a  relation  to  another  quantity  of  the  same  kind  to  which 
it  is  added,  or  from  which  it  is  subtracted ;  for  it  may  perhaps  be 
very  clear  and  intelligible  to  those  who  have  formed  to  them- 
selves some  other  idea  of  affirmative  and  negative  quantities 
different  from  that  above  defined.' 

Nothing  can  be  more  correct,  or  more  identically  logical :  +  5 
and  — 5,  standing  alone,  are  jargon  if  +5  and  — 5  are  to  be 
understood  as  without  reference  to  another  quantity.  But  those 
who  have  '  formed  to  themselves  some  other  idea '  see  meaning 


122  A   BUDGET   OF  PARADOXES. 

enough.  The  great  difficulty  of  the  opponents  of  algebra  lay  in 
want  of  power  or  will  to  see  extension  of  terms.  Maseres  is  right 
when  he  implies  that  extension,  accompanied  by  its  refusal, 
makes  jargon.  One  of  my  paradoxers  was  present  at  a  meeting 
of  the  Koyal  Society  (in  1864,  I  think)  and  asked  permis- 
sion to  make  some  remarks  upon  a  paper.  He  rambled  into 
other  things,  and,  naming  me,  said  that  I  had  written  a 
book  in  which  two  sides  of  a  triangle  are  pronounced  equal  to 
the  third.  So  they  are,  in  the  sense  in  which  the  word  is  used 
in  complete  algebra;  in  which  A  +  B  =  C  makes  A,  B,  c,  three 
sides  of  a  triangle,  and  declares  that  going  over  A  and  B,  one  after 
the  other,  is  equivalent,  in  change  of  place,  to  going  over  c  at 
once.  My  critic,  who  might,  if  he  pleased,  have  objected  to 
extension,  insisted  upon  reading  me  in  unextended  meaning. 

On  the  other  hand,  it  must  be  said  that  those  who  wrote  on 
the  other  idea  wrote  very  obscurely  about  it,  and  justified  Des 
Cartes  (De  Methodo]  when  he  said :  '  Algebram  vero,  ut  solet 
doceri,  animadverti  certis  regulis  et  numerandi  formulis  ita  esse 
contentam,  ut  videatur  potius  ars  qua3dam  confusa,  cujus  usu 
ingenium  quodam  modo  turbatur  et  obscuratur,  quam  scientia 
qua  excolatur  et  perspicacius  reddatur.'  Maseres  wrote  this 
sentence  on  the  title  of  his  own  copy  of  his  own  work,  now  before 
me  ;  he  would  have  made  it  his  motto  if  he  had  found  it  earlier. 
There  is,  I  believe,  in  Cobbett's  '  Annual  Kegister,'  an  account 
of  an  interview  between  Maseres  and  Cobbett  when  in  prison. 

The  conversation  of  Maseres  was  lively,  and  full  of  serious  anec- 
dote :  but  only  one  attempt  at  humorous  satire  is  recorded  of 
him;  it  is  an  instructive  one.  He  was  born  in  1731  (Dec.  15), 
and  his  father  was  a  refugee.  P'rench  was  the  language  of  the 
house,  with  the  pronunciation  of  the  time  of  Louis  XIV.  He 
lived  until  1824  (May  19),  and  saw  the  race  of  refugees  who 
were  driven  out  by  the  first  Eevolution.  Their  pronunciation 
differed  greatly  from  his  own ;  and  he  used  to  amuse  himself  by 
mimicking  them.  Those  who  heard  him  and  them  had  the  two 
schools  of  pronunciation  before  them  at  once;  a  thing  which 
seldom  happens.  It  might  even  yet  be  worth  while  to  examine 
the  Canadian  pronunciation. 

Maseres  went  as  Attorney-General  to  Quebec;  and  was  ap- 
pointed Cursitor  Baron  of  our  Exchequer  in  1773.  There  is  a 
curious  story  about  his  mission  to  Canada,  which  I  have  heard  as 
good  tradition,  but  have  never  seen  in  print.  The  reader  shall 
have  it  as  cheap  as  I ;  and  I  confess  I  rather  believe  it.  Maseres 
was  inveterately  honest ;  he  could  not,  at  the  bar,  boar  to  see  his 


BARON   MASERES.  123 

own  client  victorious,  when  be  knew  his  cause  was  a  bad  one. 
On  a  certain  occasion  he  was  in  a  cause  which  he  knew  would 
go  against  him  if  a  certain  case  were  quoted.  Neither  the  judge 
nor  the  opposite  counsel  seemed  to  remember  this  case,  and 
Ma  seres  could  not  help  dropping  an  allusion  which  brought  it 
out.  His  business  as  a  barrister  fell  off,  of  course.  Some  time 
after,  Mr.  Pitt  (Chatham)  wanted  a  lawyer  to  send  to  Canada  on 
a  private  mission,  and  wanted  a  very  honest  man.  Some  one 
mentioned  Maseres,  and  told  the  above  story :  Pitt  saw  that  he 
had  got  the  man  he  wanted.  The  mission  was  satisfactorily  per- 
formed, and  Maseres  remained  as  Attorney-General. 

The  'Doctrine  of  Life  Annuities'  (4to.  726  pages,  1783)  is  a 
strange  paradox.  Its  size,  the  heavy  dissertations  on  the  national 
debt,  and  the  depth  of  algebra  supposed  known,  put  it  out  of 
the  question  as  an  elementary  work,  and  it  is  unfitted  for  the 
higher  student  by  its  elaborate  attempt  at  elementary  character, 
shown  in  its  rejection  of  forms  derived  from  chances  in  favour  of 
the  average,  and  its  exhibition  of  the  separate  values  of  the 
years  of  an  annuity,  as  arithmetical  illustrations.  It  is  a  climax 
of  unsaleability,  unreadability,  and  inutility.  For  intrinsic 
nullity  of  interest,  and  dilution  of  little  matter  with  much  ink, 
I  can  compare  this  book  to  nothing  but  that  of  Claude  de  St. 
Martin,  elsewhere  mentioned,  or  the  lectures  *  On  the  Nature  and 
Properties  of  Logarithms,'  by  James  Little,  Dublin,  1830,  8vo. 
(254  heavy  pages  of  many  words  and  few  symbols),  a  wonderful 
weight  of  weariness. 

The  stock  of  this  work  on  annuities,  very  little  diminished, 
was  given  by  the  author  to  William  Frend,  who  paid  warehouse 
room  for  it  until  about  1835,  when  he  consulted  me  as  to  its 
disposal.  As  no  publisher  could  be  found  who  would  take  it 
as  a  gift,  for  any  purpose  of  sale,  it  was  consigned,  all  but  a  few 
copies,  to  a  buyer  of  waste  paper. 

Baron  Maseres's  republications  are  well  known :  the  Scriptona 
Logarithmici  is  a  set  of  valuable  reprints,  mixed  with  much 
which  might  better  have  entered  into  another  collection.  It  is 
not  so  well  known  that .  there  is  a  volume  of  optical  reprints, 
Sci^iptores  Optici,  London,  1823,  4to,  edited  for  the  veteran  of 
ninety-two  by  Mr.  Babbage  at  twenty-nine.  This  excellent 
volume  contains  James  Gregory,  Des  Cartes,  Halley,  Barrow, 
and  the  optical  writings  of  Huyghens,  the  Principia  of  the 
undulatory  theory.  It  also  contains,  by  the  sort  of  whim  in 
which  such  men  as  Maseres,  myself,  and  some  others  are  apt 
to  indulge,  a  reprint  of  '  The  great  and  new  Art  of  weighing 


124  A   BUDGET   OF  PARADOXES. 

Vanity,'  by  M.  Patrick  Mathers,  Arch-Bedel  to  the  University  of 
St.  Andrews,  Glasgow,  1672.  Professor  Sinclair,  of  Glasgow,  a 
good  man  at  clearing  mines  of  the  water  which  they  did  not 
want,  and  furnishing  cities  with  the  water  which  they  did  want, 
seems  to  have  written  absurdly  about  hydrostatics,  and  to  have 
attacked  a  certain  Sanders,  M.A.  So  Sanders,  assisted  by  James 
Gregory,  published  a  heavy  bit  of  jocosity  about  him.  This 
story  of  the  authorship  rested  on  a  note  made  in  his  copy 
by  Kobert  Gray,  M.D. ;  but  it  has  since  been  fully  confirmed  by 
a  letter  of  James  Gregory  to  Collins,  in  the  Macclesfield  Corre- 
spondence. '  There  is  one  Master  Sinclair,  who  did  write  the 
Ars  Magna  et  Nova,  a  pitiful  ignorant  fellow,  who  hath  lately 
written  horrid  nonsense  in  the  hydrostatics,  and  hath  abused  a 
master  in  the  University,  one  Mr.  Sanders,  in  print.  This  Mr. 
Sanders  ...  is  resolved  to  cause  the  Bedel  of  the  University 
to  write  against  him.  .  .  .  We  resolve  to  make  excellent  sport 
with  him.' 

On  this  I  make  two  remarks  :  First,  I  have  learnt  from  ex- 
perience that  old  notes,  made  in  books  by  their  possessors,  are 
statements  of  high  authority :  they  are  almost  always  confirmed. 
I  do  not  receive  them  without  hesitation  ;  but  I  believe  that 
of  all  the  statements  about  books  which  rest  on  one  authority, 
there  is  a  larger  percentage  of  truth  in  the  written  word  than  in 
the  printed  word.  Secondly,  I  mourn  to  think  that  when  the 
New  /Jealander  picks  up  his  old  copy  of  this  book,  and  reads  it 
by  the  associations  of  his  own  day,  he  may,  in  spite  of  the  many 
assurances  I  have  received  that  my  Athenceum  Budget  was 
amusing,  feel  me  to  be  as  heavy  as  I  feel  James  Gregory  and 
Sanders.  But  he  will  see  that  I  knew  what  was  coming,  which 
Gregory  did  not. 

It  was  left  for  William  Frend  to  prove  that  an  impugner  ol 
algebra  could  attempt  ridicule.  He  was,  in  1803,  editor  of  a 
periodical  The  Gentleman's  Monthly  Miscellany,  which  lasted 
a  few  months.  To  this,  among  other  things,  he  contributed  the 
following,  in  burlesque  of  the  use  made  of  0,  to  which  he  ob- 
jected. The  imitation  of  Eabelais,  a  writer  in  whom  he  de- 
lighted, is  good  :  to  those  who  have  never  dipped,  it  may  give 
such  a  notion  as  they  would  not  easily  get  elsewhere.  The  point 
of  the  satire  is  not  so  good.  But  in  truth  it  is  not  easy  to  make 
pungent  scoffs  upon  what  is  common  sense  to  all  mankind.  Who 
can  laugh  with  effect  at  six  times  nothing  is  nothing,  as  false  or 
unintelligible?  In  an  article  intended  for  that  undistinguishing 
know-0  the  '  general  reader,'  there  would  have  been  no  force  of 


IMITATION   OF  RABELAIS.  125 

satire,  if  division  by  0  had  been  separated  from  multiplication 
by  the  same. 

I  have  followed  the  above  by  another  squib,  by  the  same 
author,  on  the  English  language.  The  satire  is  covertly  aimed  at 
theological  phraseology;  and  any  one  who  watches  this  subject 
will  see  that  it  is  a  very  just  observation  that  the  Greek  words 
are  not  boiled  enough. 


PANTAGRUEL'S  DECISION  of  the  QUESTION  about  NOTHING. 

PANTAGRUEL  determined  to  Lave  a  snug  afternoon  with  Epistemon  and 
Panurge.  Dinner  was  ordered  to  be  set  in  a  small  parlour,  and  a 
particular  batch  of  Hermitage  with  some  choice  Burgundy  to  be  drawn 
from  a  remote  corner  of  the  cellar  upon  the  occasion.  By  way  of 
lunch,  about  an  hour  before  dinner,  Pantagruel  was  composing  his 
stomach  with  German  sausages,  reindeer's  tongues,  oysters,  brawn,  and 
half  a  dozen  different  sorts  of  English  beer  just  come  into  fashion,  when 
a  most  thundering  knocking  was  heard  at  the  great  gate,  and  from  the 
noise  they  expected  it  to  announce  the  arrival  at  least  of  the  First 
Consul,  or  king  Gargantua.  Panurge  was  sent  to  reconnoitre,  and 
after  a  quarter  of  an  hoar's  absence,  returned  with  the  news  that  the 
University  of  Pontemaca  was  waiting  his  highness's  leisure  in  the 
great  hall,  to  propound  a  question  which  had  turned  the  brains  of 
thirty-nine  students,  and  had  flung  twenty-seven  more  into  a  high 
fever.  With  all  my  heart,  says  Pantagruel,  and  swallowed  down  three 
quarts  of  Burton  ale  ;  but  remember,  it  wants  but  an  hour  of  dinner 
time,  and  the  question  must  be  asked  in  as  few  words  as  possible  ;  for 
I  cannot  deprive  myself  of  the  pleasure  I  expected  to  enjoy  in  the 
company  of  my  good  friends  for  a  set  of  mad-headed  masters.  I  wish 
brother  John  was  here  to  settle  these  matters  with  the  black  gentry. 

Having  said  or  rather  growled  this,  he  proceeded  to  the  hall  of 
ceremony,  and  mounted  his  throne  ;  Epistemon  and  Panurge  standing 
on  each  side,  but  two  steps  below  him.  Then  advanced  to  the  throne 
the  three  beadles  of  the  University  of  Pontemaca  with  their  silver 
staves  on  their  shoulders,  and  velvet  caps  on  their  heads,  and  they 
were  followed  by  three  times  three  doctors,  and  thrice  three  times 
three  masters  of  art ;  for  everything  was  done  in  Pontemaca  by  the 
number  three,  and  on  this  account  the  address  was  written  on  parch- 
ment, one  foot  in  breadth,  and  thrice  three  times  thrice  three  feet  in 
length.  The  beadles  struck  the  ground  with  their  heads  and  their 
staves  three  times  in  approaching  the  throne  ;  the  doctors  struck  the 
ground  with  their  heads  thrice  three  times,  and  the  masters  did  the 
same  thrice  each  time,  beating  the  ground  with  their  heads  thrico 
three  times.  This  was  the  accustomed  form  of  approaching  the  throne, 
time  out  of  mind,  and  it  was  said  to  be  emblematic  of  the  usual  pios- 
tration  of  science  to  the  throne  of  greatness. 


12G  A  BUDGET   OF  PAKADOXES. 

The  mathematical  professor,  after  having  spit,  and  hawked,  and 
cleared  his  throat,  and  hlown  his  nose  on  a  handkerchief  lent  to  him, 
for  he  had  forgotten  to  bring  his  own,  began  to  read  the  address.  In 
this  he  was  assisted  by  three  masters  of  arts,  one  of  whom,  with  a 
silver  pen,  pointed  out  the  stops ;  the  second  with  a  small  stick  rapped 
his  knuckles  when  he  was  to  raise  or  lower  his  voice ;  and  a  third 
pulled  his  hair  behind  when  he  was  to  look  Pantagruel  in  the  face. 
Pantagruel  began  to  chafe  like  a  lion  :  he  turned  first  on  one  side,  then 
on  the  other  :  he  listened  and  groaned,  and  groaned  and  listened,  and 
was  in  the  utmost  cogitabundity  of  cogitation.  His  countenance 
began  to  brighten,  when,  at  the  end  of  an  hour,  the  reader  stammered 
out  these  words : 

'  It  has  therefore  been  most  clearly  proved,  that  as  all  matter  may 
be  divided  into  parts  infinitely  smaller  than  the  infinitely  smallest  part 
of  the  infinitesimal  of  nothing,  so  nothing  has  all  the  properties  of 
something,  and  may  become,  by  just  and  lawful  right,  susceptible  of 
addition,  subtraction,  multiplication,  division,  squaring,  and  cubing  : 
that  it  is  to  all  intents  and  purposes  as  good  as  anything  that  has 
been,  is,  or  can  be  taught  in  the  nine  universities  of  the  land,  and  to 
deprive  it  of  its  rights  is  a  most  cruel  innovation  and  usurpation, 
tending  to  destroy  all  just  subordination  in  the  world,  making  all 
universities  superfluous,  levelling  vice-chancellors,  doctors,  and  proctors, 
masters,  bachelors,  and  scholars,  to  the  mean  and  contemptible  state  of 
butchers  and  tallow-chandlers,  bricklayers  and  chimney-sweepers,  who, 
if  it  were  pot  for  these  learned  mysteries,  might  think  that  they  knew 
as  much  as"  their  betters.  Every  one  then,  who  has  the  good  of  science 
at  heart,  must  pray  for  the  interference  of  his  highness  to  put  a  stop 
to  all  the  disputes  about  nothing,  and  by  his  decision  to  convince  all 
gainsayers  that  the  science  of  nothing  is  taught  in  the  best  manner  in 
the  universities,  to  the  great  edification  and  improvement  of  all  the 
youth  in  the  land.' 

Here  Pantagruel  whispered  in  the  ear  of  Panurge,  who  nodded  to 
Epistemon,  and  they  two  left  the  assembly,  and  did  not  return  for  an 
hour,  till  the  orator  had  finished  his  task.  The  three  beadles  had 
thrice  struck  the  ground  with  their  heads  and  staves,  the  doctors  had 
finished  their  compliments,  and  the  masters  Were  making  their  twenty- 
seven  prostrations.  Epistemon  and  Panurge  went  up  to  Pantagruel, 
whom  they  found  fast  asleep  and  snoring ;  nor  could  he  be  roused  but 
by  as  many  tugs  as  there  had  been  bowings  from  the  corps  of  learning. 
At  last  he  opened  his  eyes,  gave  a  good  stretch,  made  half  a  dozen 
yawns,  and  called  for  a  stoup  of  wine.  I  thank  you,  my  masters,  says 
be ;  so  sound  a  nap  I  have  not  had  since  I  came  from '  the  island  of 
Priestfolly.  Have  you  dined,  my  masters  ?  They  answered  the 
question  by  as  many  bows  as  at  entrance  ;  but  his  highness  left  them 
to  the  care  of  Panurge,  and  retired  to  the  little  parlour  with  Epistemon, 
where  they  burst  into  a  fit  of  laughter,  declaring  that  this  learned 
Buragouin  about  nothing  was  just  as  intelligible  as  the  lawyer's 


IMITATION   OF   RABELAIS.  127 

Galimathias.  Panurge  conducted  the  learned  body  into  a  large  saloon, 
and  each  in  his  way  hearing  a  clattering  of  plates  and  glasses,  con- 
gratulated himself  on  his  approaching  good  cheer.  There  they  wero 
left  by  Panurge,  who  took  his  chair  by  Pantagrnel  just  as  the  spup 
was  removed,  but  he  made  up  for  the  want  of  that  part  of  his  dinner 
by  a  pint  of  Champagne.  The  learning  of  the  university  had  whetted 
their  appetites  ;  what  they  each  ate  it  is  needless  to  recite  ;  good  wine, 
good  stories,  and  hearty  laughs  went  round,  and  three  hours  elapsed 
before  one  soul  of  them  recollected  the  hungry  students  of  Pontemaca. 

Epistemon  reminded  them  of  the  business  in  hand,  and  orders  were 
given  for  a  fresh  dozen  of  hermitage  to  be  put  upon  table,  and  the 
royal  attendants  to  get  ready.  As  soon  as  the  dozen  bottles  were 
emptied,  Pantagruel  rose  from  table,  the  royal  trumpets  sounded,  and 
he  was  accompanied  by  the  great  officers  of  his  court  into  the  large 
dining  hall,  where  was  a  table  with  forty-two  covers.  Pantagruel  sat 
at  the  head,  Epistemon  at  the  bottom,  and  Panurge  in  the  middle, 
opposite  an  immense  silver  tureen,  which  would  hold  fifty  gallons  of 
soup.  The  wise  men  of  Pontemaca  then  took  their  scats  according  to 
seniority.  Every  countenance  glistened  with  delight ;  the  music  struck 
up  ;  the  dishes  were  uncovered.  Panurge  had  enough  to  do  to  handle 
the  immense  silver  ladle  :  Pantagruel  and  Epistemon  had  no  time  for 
eating,  they  were  fully  employed  in  carving.  The  bill  of  fare  announced 
the  names  of  a  hundred  different  dishes.  From  Panurge's  ladle  came 
into  the  soup  plate  as  much  as  he  took  every  time  out  of  the  tureen ; 
and  as  it  was  the  rule  of  the  court  that  every  one  should  appear  to  eat, 
as  long  as  he  sat  at  table,  there  was  the  clattering  of  nine  and  thirty 
spoons  against  the  silver  soup-plates  for  a  quarter  of  an  hour.  They 
were  then  removed,  and  knives  and  forks  were  in  motion  for  half  an 
hour.  Glasses  were  continually  handed  round  in  the  mean  time,  and 
then  everything  was  removed,  except  the  great  tureen  of  soup.  The 
second  course  was  now  served  up,  in  dispatching  which  half  an  hour 
was  consumed ;  and  at  the  conclusion  the  wise  men  of  Pontemaca  had 
just  as  much  in  their  stomachs  as  Pantagruel  in  his  head  from  their 
address :  for  nothing  was  cooked  up  for  them  in  every  possible  shape 
that  Panurge  could  devise. 

Wine-glasses,  large  decanters,  fruit  dishes,  and  plates  were  now  set 
on.  Pantagruel  and  Epistemon  alternately  gave  bumper  toasts :  the 
University  of  Pontemaca,  the  eye  of  the  world,  the  mother  of  taste  and 
good  sense  and  universal  learning,  the  patroness  of  utility,  and  the 
second  only  to  Pantagruel  in  wisdom  and  virtue  (for  these  were  her 
titles),  was  drank  standing  with  thrice  three  times  three,  and  huzzas 
and  clatterings  of  glasses  ;  but  to  such  wine  the  wise  men  of  Pontemaca 
had  not  been  accustomed  ;  and  though  Pantagruel  did  not  suffer  one 
to  rise  from  table  till  the  eighty-first  glass  had  been  emptied,  not  even 
the  weakest  headed  master  of  arts  felt  his  head  in  the  least  indisposed. 
The  decanters  indeed  were  often  removed,  but  they  were  brought  back 
replenished,  filled  always  with  nothing. 


128  A  BUDGET  OF  PAKADOXES. 

Silence  was  now  proclaimed,  and  in  a  trice  Panurge  leaped  into  the 
large  silver  tureen.  Thence  he  made  his  bows  to  Pantagruel  and  the 
whole  company,  and  commenced  an  oration  of  signs,  which  lasted  au. 
hour  and  a  half,  and  in  which  he  went  over  all  the  matter  contained 
in  the  Pontemacan  address ;  and  though  the  wise  men  looked  very 
serious  during  the  whole  time,  Pantagruel  himself  and  his  whole  court 
could  not  help  indulging  in  repeated  bursts  of  laughter.  It  was 
universally  acknowledged  that  he  excelled  himself,  and  that  the  ar- 
guments by  which  he  beat  the  English  masters  of  arts  at  Paris  were 
nothing  to  the  exquisite  selection  of  attitudes  which  he  this  day 
assumed.  The  greatest  shouts  of  applause  were  excited  when  he  was 
running  thrice  round  the  tureen  on  its  rim,  with  his  left  hand  holding 
his  nose,  and  the  other  exercising  itself  nine  and  thirty  times  on  his 
back.  In  this  attitude  he  concluded  with  his  back  to  the  pro- 
fessor of  mathematics  ;  and  at  the  instant  he  gave  his  last  flap,  by  a 
sudden  jump,  and  turning  heels  over  head  in  the  air,  he  presented 
himself  face  to  face  to  the  professor,  and  standing  on  his  left  leg,  with 
his  left  hand  holding  his  nose,  he  presented  to  him,  in  a  white  satin 
bag,  Pantagruel's  royal  decree.  Then  advancing  his  right  leg,  he 
fixed  it  on  the  professor's  head,  and  after  three  turns,  in  which  he 
clapped  his  sides  with  both  hands  thrice  three  times,  down  he 
leaped,  and  Pantagruel,  Epistemon,  and  himself  took  their  leaves  of  the 
wise  men  of  Pontemaca. 

The  wise  men  now  retired,  and  by  royal  orders  were  accompanied 
by  a  guard,  and  according  to  the  etiquette  of  the  court,  no  one  having 
a  royal  order  could  stop  at  any  public  house  till  it  was  delivered.  The 
procession  arrived  at  Pontemaca  at  nine  o'clock  the  next  morning,  and 
the  sound  of  bells  from  every  church  and  college  announced  their 
arrival.  The  congregation  was  assembled ;  the  royal  decree  was 
saluted  in  the  same  manner  as  if  his  highness  had  been  there  in 
person ;  and  after  the  proper  ceremonies  had  been  performed,  the 
satin  bag  was  opened  exactly  at  twelve  o'clock.  A  finely  emblazoned 
roll  was  drawn  forth,  and  the  public  orator  read  to  the  gaping  assembly 
the  following  words  : 

'  They  who  can  make  something  out  of  nothing  shall  have  nothing 
to  eat  at  the  court  of — PANTAGKUEL.' 


ORIGIN  of  the  ENGLISH  LANGUAGE,  related  ly  a  SWEDE. 

SOME  months  ago  in  a  party  in  Holland,  consisting  of  natives  of  various 
countries,  the  merit  of  their  respective  languages  became  a  topic  of 
conversation.  A  Swede,  who  had  been  a  great  traveller,  and  could 
converse  in  most  of  the  modern  languages  of  Europe,  laughed  very 
heartily  at  an  Englishman,  who  had  ventured  to  speak  in  praise  of  the 
tongue  of  his  dear  country.  I  never  had  any  trouble,  says  he,  in  learning 
English.  To  my  very  great  surprise,  the  moment  I  sat  foot  on  shore 


ORIGIN  OF  ENGLISH;  A  FABLE.  129 

at  Gravesend,  I  found  out,  that  I  could  understand,  with  very  little 
trouble,  every  word  that  was  said.  It  was  a  mere  jargon,  made  up  of 
German,  French,  and  Italian,  with  now  and  then  a  word  from  the 
Spanish,  Latin,  or  Greek.  I  had  only  to  bring  my  mouth  to  their 
mode  of  speaking,  which  was  done  with  ease  in  less  than  a  week,  and 
I  was  every  where  taken  for  a  true-born  Englishman ;  a  privilege  by 
the  way  of  no  small  importance  in  a  country,  where  each  man,  God 
knows  why,  thinks  his  foggy  island  superior  to  any  other  part  of  the 
world :  and  though  his  door  is  never  free  from  some  dun  or  other 
coming  for  a  tax,  and  if  he  steps  out  of  it  he  is  sure  to  be  knocked 
down  or  to  have  his  pocket  picked,  yet  he  has  the  insolence  to  think 
every  foreigner  a  miserable  slave,  and  his  country  the  seat  of  every 
thing  wretched.  They  may  talk  of  liberty  as  they  please,  but  Spain 
or  Turkey  for  my  money :  barring  the  bowstring  and  the  inquisition, 
they  are  the  most  comfortable  countries  under  heaven,  and  you  need 
not  be  afraid  of  either,  if  you  do  not  talk  of  religion  and  politics.  I  do 
not  see  much  difference  too  in  this  respect  in  England,  for  when  I  was 
there,  one  of  their  most  eminent  men  for  learning  was  put  in  prison 
for  a  couple  of  years,  and  got  his  death  for  translating  one  of  j9Ssop's 
fables  into  English,  which  every  child  in  Spain  and  Turkey  is  taught, 
as  soon  as  he  comes  out  of  his  leading  strings.  Here  all  the  company 
unanimously  cried  out  against  the  Swede,  that  it  was  impossible  :  for  in 
England,  the  land  of  liberty,  the  only  thing  its  worst  enemies  could 
pay  against  it,  was,  that  they  paid  for  their  liberty  a  much  greater 
price  than  it  was  worth. — Every  man  there  had  a  fair  trial  accord- 
ing to  laws,  which  every  body  could  understand  ;  and  the  judges  were 
cool,  patient,  discerning  men,  who  never  took  the  part  of  the  crown 
against  the  prisoner,  but  gave  him  every  assistance  possible  for  his 
defence. 

The  Swede  was  borne  down,  but  not  convinced ;  and  he  seemed 
determined  to  spit  out  all  his  venom.  Well,  says  he,  at  any  rate  you 
will  not  deny  that  the  English  have  not  got  a  language  of  their  own, 
and  that  they  came  by  it  in  a  very  odd  way.  Of  this  at  least  I  am 
certain,  for  the  whole  history  was  related  to  me  by  a  witch  in  Lapland, 
whilst  I  was  bargaining  for  a  wind.  Here  the  company  were  all  in 
unison  again  for  the  story. 

In  antient  times,  said  the  old  hag,  the  English  occupied  a  spot  in 
Tartary,  where  they  lived  sulkily  by  themselves,  unknowing  and  un- 
known. By  a  great  convulsion  that  took  place  in  China,  the  inhabit- 
ants of  that  and  the  adjoining  parts  of  Tartary  were  driven  from  their 
seats,  and  after  various  wanderings  took  up  their  abode  in  Germany. 
During  this  time  no  body  could  understand  the  English,  for  they  did 
not  talk,  but  hissed  like  so  many  snakes.  The  poor  people  felt  uneasy 
under  this  circumstance,  and  in  one  of  their  parliaments,  or  rather 
hissing  meetings,  it  was  determined  to  seek  for  a  remedy :  and  an 
embassy  was  sent  to  some  of  our  sisterhood  then  living  on  Mount 
Hccla.  They  were  put  to  a  nonplus,  and  summoned  the  Devil  to  their 

K 


130  A  BUDGET    OF   PAEADOXE8. 

relief.  To  him  the  English  presented  their  petitions,  and  explained 
their  sad  case  ;  and  he,  upon  certain  conditions,  promised  to  befriend 
them,  and  to  give  them  a  language.  The  poor  Devil  was  little  aware 
of  what  he  had  promised  ;  but  he  is,  as  all  the  world  knows,  a  man  of 
too  much  honour  to  break  his  word.  Up  and  down  the  world  then  he 
went  in  quest  of  this  new  language  :  visited  all  the  universities,  and 
all  the  schools,  and  all  the  courts  of  law,  and  all  the  play-houses,  and 
all  the  prisons ;  never  was  poor  devil  so  fagged.  It  would  have  made 
your  heart  bleed  to  see  him.  Thrice  did  he  go  round  the  earth  in 
every  parallel  of  latitude ;  and  at  last,  wearied  and  jaded  out,  back 
came  he  to  Hecla  in  despair,  and  would  have  thrown  himself  into  the 
volcano,  if  he  had  been  made  of  combustible  materials.  Luckily  at 
that  time  our  sisters  were  engaged  in  settling  the  balance  of  Europe ; 
and  whilst  they  were  looking  over  projects,  and  counter-projects,  and 
ultimatums,  and  post  ultimatums,  the  poor  Devil,  unable  to  assist  them, 
was  groaning  in  a  corner  and  ruminating  over  his  sad  condition. 

On  a  sudden,  a  hellish  joy  overspread  his  countenance;  up  he 
jumped,  and,  like  Archimedes  of  old,  ran  like  a  madman  amongst  the 
thi-ong,  turning  over  tables,  and  papers,  and  witches,  roaring  out  for  a 
full  hour  together  nothing  else  but  'tis  found,  'tis  found  !  Away  were 
sent  the  sisterhood  in  every  direction,  some  to  traverse  all  corners  of 
the  earth,  and  others  to  prepare  a  larger  caldron  than  had  ever  yet 
been  set  upon  Hecla.  The  affairs  of  Europe  were  at  a  stand  :  its 
balance  was  thrown  aside ;  prime  ministers  and  ambassadors  were 
every  where  in  the  utmost  confusion ;  and,  by  the  way,  they  have 
never  been  able  to  find  the  balance  since  that  time,  and  all  the  fine 
speeches  upon  the  subject,  witli  which  your  newspapers  are  every  now 
and  then  filled,  are  all  mere  hocus-pocus  and  rhodomontade.  How- 
ever, the  caldron  was  soon  set  on,  and  the  air  was  darkened  by  witches 
riding  on  broomsticks,  bringing  a  couple  of  folios  under  each  arm,  and 
across  each  shoulder.  I  remember  the  time  exactly:  it  was  just  as  the 
council  of  Nice  had  broken  up,  so  that  they  got  books  and  papers  there 
dog  cheap ;  but  it  was  a  bad  thing  for  the  poor  English,  as  these  were 
the  worst  materials  that  entered  into  the  caldron.  Besides,  as  the 
Devil  wanted  some  amusement,  and  had  not  seen  an  account  of  the 
transactions  of  this  famous  council,  he  had  all  the  books  brought  from 
it  laid  before  him,  and  split  his  sides  almost  with  laughing,  whilst  he 
was  reading  the  speeches  and  decrees  of  so  many  of  his  old  friends  and 
acquaintance.  All  this  while  the  witches  were  depositing  their  loads 
in  the  great  caldron.  There  were  books  from  the  Dalai  Lama,  and 
from  China :  there  were  books  from  the  Hindoos,  and  tallies  from  the 
Caffres  :  there  were  paintings  from  Mexico,  and  rocks  of  hieroglyphics 
from  Egypt :  the  last  country  supplied  besides  the  swathings  of  two 
thousand  mummies,  and  four-fifths  of  the  famed  library  of  Alexandi-ia. 
Bubble !  bubble  !  toil  and  trouble  !  never  was  a  day  of  more  labour 
and  anxiety  ;  and  if  our  good  master  had  but  flung  in  the  Greek  books 
at  the  proper  time,  they  would  have  made  a  complete  job  of  it.  He 


EARLY   GENIUS.  131 

was  a  little  too  impatient :  as  the  caldron  frothed  up,  he  skimmed  it 
off  with  a  great  ladle,  and  filled  some  thousands  of  our  wind-bags 
with  the  froth,  which  the  English  with  great  joy  carried  back  to  their 
own  country.  These  bags  were  sent  to  every  district :  the  chiefs  first 
took  their  fill,  and  then  the  common  people ;  hence  they  now  speak 
a  language  which  no  foreigner  can  understand,  unless  he  has  learned 
half  a  dozen  other  languages ;  and  the  poor  people,  not  one  in  ten, 
understand  a  third  part  of  what  is  said  to  them.  The  hissing,  how- 
ever, they  have  not  entirely  got  rid  of,  and  every  seven  years,  when 
the  Devil,  according  to  agreement,  pays  them  a  visit,  they  entertain 
him  at  their  common  halls  and  county  meetings  with  their  original 
language. 

The  good  natured  old  hag  told  me  several  other  circumstances, 
relative  to  this  curious  transaction,  which,  as  there  is  an  Englishman 
in  company,  it  will  be  prudent  to  pass  over  in  silence :  but  I  cannot 
help  mentioning  one  thing  which  she  told  me  as  a  very  great  secret. 
You  know,  says  she  to  me,  that  the  English  have  more  religions  among 
them  than  any  other  nation  in  Europe,  and  that  there  is  more  teaching 
and  sermonizing  with  them  than  in  any  other  country.  The  fact  is 
this  ;  it  matters  not  who  gets  up  to  teach  them,  the  hard  words  of  the 
Greek  were  not  sufficiently  boiled,  and  whenever  they  get  into  a 
sentence,  the  poor  people's  brains  are  turned,  and  they  know  no  more 
what  the  preacher  is  talking  about,  than  if  he  harangued  them  in 
Arabic.  Take  my  word  for  it  if  you  please  ;  but  if  not,  when  you  get 
to  England,  desire  the  bettermost  sort  of  people  that  you  are  acquainted 
with  to  read  to  you  an  act  of  parliament,  which  of  course  is  written  in 
the  clearest  and  plainest  stile  in  which  any  thing  can  be  written,  and 
you  will  find  that  not  one  in  ten  will  be  able  to  make  tolerable  sense 
of  it.  The  language  would  have  been  an  excellent  language,  if  it  had 
not  been  for  the  council  of  Nice,  and  the  words  had  been  well  boiled. 

Here  the  company  burst  out  into  a  fit  of  laughter.  The  Englishman 
got  up  and  shook  hands  with  the  Swede :  si  non  e  vero,  said  he,  e  ben 
trovato.  But,  however  I  may  laugh  at  it  here,  I  would  not  advise 
you  to  tell  this  story  on  the  other  side  of  the  water.  So  here's  a 
bumper  to  Old  England  for  ever,  and  God  save  the  king.' 


The  accounts  given  of  extraordinary  children  and  adolescents 
frequently  defy  credence.  I  will  give  two  well-attested  instances. 

The  celebrated  mathematician,  Alexis  Claude  Clairault  (now 
Clairaut)  was  certainly  born  in  May,  1713.  His  treatise  on 
curves  of  double  curvature  (printed  in  1731)  received  the  appro- 
bation of  the  Academy  of  Sciences,  August  23,  1729.  Fontenelle, 
in  his  certificate  of  this,  calls  the  author  sixteen  years  of  age,  and 

K    2 


A  BUDGET   OF  PARADOXES. 

does  not  strive  to  exaggerate  the  wonder,  as  he  might  have  done, 
by  reminding  his  readers  that  this  work,  of  original  and  sustained 
mathematical  investigation,  must  have  been  coming  from  the  pen 
at  the  ages  of  fourteen  and  fifteen.  The  truth  was,  as  attested 
by  De  Molieres,  Clairaut  had  given  public  proofs  of  his  power  at 
twelve  years  old.  His  age  being  thus  publicly  certified,  all  doubt 
is  removed :  say  he  had  been — though  great  wonder  would  still 
have  been  left — twenty-one  instead  of  sixteen,  his  appearance, 
and  the  remembrances  of  his  friends,  schoolfellows,  &c.,  would 
have  made  it  utterly  hopeless  to  knock  off  five  years  of  that  age 
while  he  was  on  view  in  Paris  as  a  young  lion.  De  Molieres,  who 
examined  the  work  officially  for  the  Garde  des  Sceaux,  is  trans- 
ported beyond  the  bounds  of  official  gravity,  and  says  that  it  *  ne 
merite  pas  seulement  d'etre  imprime,  mais  d'etre  admire  comme 
im  prodige  d'imagination,  de  conception,  et  de  capacite.' 

That  Blaise  Pascal  was  born  in  June,  1623,  is  perfectly  well 
established  and  uncontested.  That  he  wrote  his  conic  sections  at 
the  age  of  sixteen  might  be  difficult  to  establish,  though  tolerably 
well  attested,  if  it  were  not  for  one  circumstance,  for  the  book 
was  not  published.  The  celebrated  theorem,  Pascal's  hexagram, 
makes  all  the  rest  come  very  easy.  Now  Curabelle,  in  a  work 
published  in  1644,  sneers  at  Desargues,  whom  he  quotes,  for 
having,  in  1642,  deferred  a  discussion  until  cette  grande  proposi- 
tion nommee  la  Pascale  vei^ra  le  jour.  That  is,  by  the  time 
Pascal  was  nineteen,  the  hexagram  was  circulating  under  a  name 
derived  from  the  author.  The  common  story  about  Pascal, 
given  by  his  sister,  is  an  absurdity  which  no  doubt  has  prejudiced 
many  against  tales  of  early  proficiency.  He  is  made,  when  quite 
a  boy,  to  invent  geometry  in  the  order  of  Euclid's  propositions  : 
as  if  that  order  were  natural  sequence  of  investigation.  The 
hexagram  at  ten  years  old  would  be  a  hundred  times  less  un- 
likely. 

The  instances  named  are  painfully  astonishing :  I  give  one 
which  has  fallen  out  of  sight,  because  it  will  preserve  an  imperfect 
biography.  John  Wilson  is  Wilson  of  that  Ilk,  that  is,  of 
Wilson's  Theorem.-.  It  is  this  :  If  p  be  a  prime  number,  the 
product  of  all  the  numbers  up  to  p  -1,  increased  by  1,  is  divisible 
without  remainder  by  p.  All  mathematicians  know  this  as 
Wilson's  theorem,  but  few  know  who  Wilson  was.  He  was  born 
August  6,  1741,  at  the  Howe  in  Applethwaite,  and  he  was  heir 
to  a  small  estate  at  Troutbeck  in  Westmoreland.  He  was  sent  to 
Peterhouse,  at  Cambridge,  and,  while  an  undergraduate  was 
considered  stronger  in  algebra  than  any  one  in  the  University, 


JOHN  WILSON— WILLIAM  MORGAN— MRS.  FRY.  133 

except  Professor  Waring,  one  of  the  most  powerful  algebraists  of 
the  century.1     He  was  the  senior  wrangler  of  1761,  and  was  then 
for  some  time  a  private  tutor.     When  Paley,  then  in  his  third 
year,  determined  to  make  a  push  for  the  senior  wranglership, 
which  he  got,  Wilson  was  recommended  to  him  as  a  tutor.     Both 
were  ardent  in  their  work,  except  that  sometimes  Paley,  when  he 
came  for  his  lesson,  would  find  gone  a  fishing  written  on  his 
tutor's  outer  door:  which  was  insult  added  to  injury,  for  Paley 
was  very  fond  of  fishing.     Wilson  soon  left  Cambridge,  and  went 
to    the   bar.     He   practised  on  the  northern  circuit  with  great 
success ;  and,  one  day,  while  passing  his  vacation  on  his  little 
property   at   Troutbeck,  he   received  information,  to   his   great 
surprise,  that  Lord  Thurlow,  with  whom  he  had  no  acquaintance, 
had  recommended  him  to  be  a  Judge  of  the  Court  of  Common 
Pleas.     He  died,  Oct.  18,   1793,  with    a  very  high  reputation 
as  a  lawyer  and  a  Judge.     These  facts  are  partly  from  Meadley'a 
'  Life  of  Paley,'  no  doubt   from  Paley  himself,  partly  from  the 
Gentleman's  Magazine,  and  from  an  epitaph  written  by  Bishop 
Watson.     Wilson    did   not  publish  anything :    the   theorem  by 
which  he  has  cut  his  name  in  the  theory  of  numbers  was  com- 
municated to  Waring,  by  whom  it  was  published.     He  married, 
in    1788,  a  daughter  of  Serjeant  Adair,  and  left  issue.     Had  a 
family,  many  will  say :  but  a  man  and  his  wife  are  a  family,  even 
without  children.     An  actuary  may  be  allowed  to  be  accurate  in 
this  matter,  of  which  I  was  reminded  by  what  an  actuary  wrote 
of  another  actuary.     William  Morgan,  in  the  life  of  his  uncle 
Dr.  Richard  Price,  says  that  the  Doctor  and  his  wife  were  '  never 
blessed  with  an  addition  to  their  family.'     I  never  met  "with  such 
accuracy  elsewhere.     Of  William  Morgan  I  add  that  my  surname 
and  pursuits  have  sometimes,  to  my  credit  be  it  said,  made  a 
confusion   between   him   and   me.      Dates   are   nothing   to  the 
xuistaken  ;    the  last  three  years  of  Morgan's  life  were  the  first 
three  years  of  my  actuary-life  (1830-33).     The  mistake  was  to 
my  advantage  as  well  as  to  my  credit.     I  owe  to  it  the  acquaint- 
ance of  one  of  the  noblest  of  the  human  race,  I  mean  Elizabeth 
Fry,  who  came  to  me  for  advice  about  a  philanthropic  design, 
which  involved  life  questions,  under  a  general  impression  that 
some  Morgan  had  attended  to  such  things.2 

1  He  wrote,  in  1760,  a  tract  in  defence  of  Waring,  a  point  of  whose  algebra  had 
been  assailed  by  a  Dr.  Powell.     Waring  wrote  another  tract  of  the  same  date. 

2  Mrs.  Fry  certainly  believed  that  the  writer  was  the  old  actuary  of  the  Equitable, 
when  she  first  consulted  him  upon  the  benevolent  Assurance  project ;  but  we  were 
introduced  to  her  by  our  old  and  dear  friend  Lady  Noel  Byron,  by  whom  she  had 


134  A  BUDGET  OF  PARADOXES. 


A  treatise  on  the  sublime  science  of  heliography,  satisfactorily 
demonstrating  our  great  orb  of  light,  the  sun,  to  be  absolutely 
no  other  than  a  body  of  ice !  Overturning  all  the  received 
systems  of  the  universe  hitherto  extant ;  proving  the  celebrated 
and  indefatigable  Sir  Isaac  Newton,  in  his  theory  of  the  solar 
system,  to  be  as  far  distant  from  the  truth,  as  any  of  the 
heathen  authors  of  Greece  or  Borne.  By  Charles  Palmer,  Gent. 
London,  1798,  8vo. 

Mr.  Palmer  burned  some  tobacco  with  a  burning  glass,  saw 
that  a  lens  of  ice  would  do  as  well,  and  then  says — 

'  If  we  admit  that  the  sun  could  be  removed,  and  a  terrestrial  body 
of  ice  placed  in  its  stead,  it  would  produce  the  same  effect.  The  sun 
is  a  crystaline  body  receiving  the  radience  of  God,  and  operates  on  this 
earth  in  a  similar  manner  as  the  light  of  the  sun  does  when  applied  to 
a  convex  mirror  or  glass.' 

Nov.  10,  1801.  The  Eev.  Thomas  Cormouls,  minister  of 
Tettenhall,  addressed  a  letter  to  Sir  Wm.  Herschel,  from  which  I 
extract  the  following : — 

Here  it  may  be  asked,  then,  how  came  the  doctrines  of  Newton  to 
solve  all  astronomic  Phenomina,  and  all  problems  concerning  the  same, 
both  a  parte  ante  and  a  parte  post.  It  is  answered  that  he  certainly 
wrought  the  principles  he  made  use  of  into  strickt  analogy  with  the 
real  Phenomina  of  the  heavens,  and  that  the  rules  and  results  arizing 
from  them  agree  with  them  and  resolve  accurately  all  questions  con- 
cerning them.  Though  they  are  not  fact  and  true,  or  nature,  but 
analogous  to  it,  in  the  manner  of  the  artificial  numbers  of  logarithms, 
sines,  &c.  A  very  important  question  arises  here,  Did  Newton  mean 
to  impose  upon  the  world  ?  By  no  means :  he  received  and  used  the 
doctrines  reddy  formed ;  he  did  a  little  extend  and  contract  his  prin- 
ciples when  wanted,  and  commit  a  few  oversights  of  consequences.  But 
when  he  was  very  much  advanced  in  life,  he  suspected  the  fundamental 
nullity  of  them  :  but  I  have  from  a  certain  anecdote  strong  ground  to 
believe  that  he  knew  it  before  his  decease,  and  intended  to  have  re- 
tracted his  error.  But,  however,  somebody  did  deceive,  if  not  wilfully, 
neglently  at  least.  That  was  a  man  to  whom  the  world  has  great 
obligations  too.  It  was  no  less  a  philosopher  than  Galileo. 

That  Newton  wanted  to  retract  before  his  death,  is  a  notion 
not   uncommon  among  paradoxers.      Nevertheless,   there  is  no 

been  long  known  and  venerated,  and  who  referred  her  to  Mr.  De  Morgan  for  advice. 
An  unusual  degree  of  confidence  in,  and  appreciation  of  each  other,  arose  on  their 
first  meeting  between  the  two,  who  had  so  much  that  was  externally  different,  and  so 
much  that  was  essentially  alike,  in  their  natures. — (Ed.) 


BISHOP  WILKINS'S   WORKS,  135 

retraction  in  the  third  edition  of  the  '  Principia,'  published  when 
Newton  was  eighty-four  years  old !  The  moral  of  the  above  is, 
that  a  gentleman  who  prefers  instructing  William  Herschel  to 
learning  how  to  spell,  may  find  a  proper  niche  in  a  proper  place, 
for  warning  to  others.  It  seems  that  gravitation  is  not  truth, 
but  only  the  logarithm  of  it. 

The  mathematical  and  philosophical  works  of  the  Right  Rev. 
John  Wilkins  ...  In  two  volumes.     London,  1802,  8vo. 

This  work,  or  at  least  part  of  the  edition — all  for  aught  I  know 
— is  printed  on  wood ;  that  is,  on  paper  made  from  wood-pulp. 
It  has  a  rough  surface,  and  when  held  before  a  candle  is  of  very 
unequal  transparency.  There  is  in  it  a  reprint  of  the  works  on 
the  earth  and  moon.  The  discourse  on  the  possibility  of  going 
to  the  moon,  in  this  and  the  edition  of  1 640,  is  incorporated : 
but  from  the  account  in  the  life  prefixed,  and  a  mention  by 
D'Israeli,  I  should  suppose  that  it  had  originally  a  separate  title- 
page,  and  some  circulation  as  a  separate  tract.  Wilkins  treats 
this  subject  half  seriously,  half  jocosely ;  he  has  evidently  not 
quite  made  up  his  mind.  He  is  clear  that  '  arts  are  not  yet  come 
to  their  solstice,'  and  that  posterity  will  bring  hidden  things  to 
light.  As  to  the  difficulty  of  carrying  food,  he  thinks,  scoffing 
Puritan  that  he  is,  the  Papists  may  be  trained  to  fast  the  voyage, 
or  may  find  the  bread  of  their  Eucharist  '  serve  well  enough  for 
their  viaticum.'  He  also  puts  the  case  that  the  story  of  Do- 
mingo Gonsales  may  be  realized,  namely,  that  wild  geese  find 
their  way  to  the  moon.  It  will  be  remembered — to  use  the 
usual  substitute  for,  It  has  been  forgotten — that  the  posthumous 
work  of  Bishop  Francis  Godwin  of  Llandaff  was  published  in 
1638,  the  very  year  of  Wilkins's  first  edition,  in  time  for  him  to 
mention  it  at  the  end.  Godwin  makes  Domingo  Gronsales  get  to 
the  moon  in  a  chariot  drawn  by  wild  geese,  and,  as  old  books 
would  say,  discourses  fully  on  that  head.  It  is  not  a  little 
amusing  that  Wilkins  should  have  been  seriously  accused  of 
plagiarizing  Godwin,  Wilkins  writing  in  earnest,  or  nearly  so, 
and  Godwin  writing  fiction.  It  may  serve  to  show  philosophers 
how  very  near  pure  speculation  comes  to  fable.  From  the 
sublime  to  the  ridiculous  there  is  but  a  step :  which  is  the  sub- 
lime, and  which  the  ridiculous,  every  one  must  settle  for  himself. 
With  me,  good  fiction  is  the  sublime,  and  bad  speculation  the 
ridiculous.  The  number  of  bishops  in  my  list  is  small.  I 
might,  had  I  possessed  the  book,  have  opened  the  list  of  quad- 
rators  with  an  Archbishop  of  Canterbury,  or  at  least  with  a 


136  A  BUDGET   OF  PARADOXES. 

divine  who  was  not  wholly  not  archbishop.  Thomas  Bradwardine 
(Bragvardinus,  Bragadinus)  was  elected  in  1348  ;  the  Pope  put 
in  another,  who  died  unconsecrated  ;  and  Bradwardine  was  again 
elected  in  1 349,  and  lived  five  weeks  longer,  dying,  I  suppose, 
unconfirmed  and  unconsecrated.  Leland  says  he  held  the  see  a 
year,  unus  tantum  annulus,  which  seems  to  be  a  confusion : 
the  whole  business,  from  the  first  election,  took  about  a  year. 
He  squared  the  circle,  and  his  performance  was  printed  at  Paris 
in  1494.  I  have  never  seen  it,  nor  any  work  of  the  author, 
except  a  tract  on  proportion. 

As  Bradwardine's  works  are  very  scarce  indeed,  I  give  two  titles 
from  one  of  the  Libri  catalogues. 

'  ARITHMETIC.  BRAUARDINI  (Thomas)  Ai-ithmetica  speculativa  revisa 
et  correcta  a  Petro  Sanchez  Ciruelo  Aragonesi,  black  letter, 
elegant  woodcut  title-page,  YERY  RARE,  folio.  Parisiis,  per  Thomam 
Anguelast  {pro  Olivier  Senant),  s.a.  circa  1510. 

'  This  book,  by  Thomas  Bradwardine,  Archbishop  of  Canterbury, 
must  be  exceedingly  scarce  as  it  has  escaped  the  notice  of  Pro- 
fessor De  Morgan,  who,  in  his  Arithmetical  Books,  speaks  of  a 
treatise  of  the  same  author  on  proportions,  printed  at  Vienna  in 
1515,  but  does  not  mention  the  present  work. 

'Bradwardine  (Archbp.  T.).  Brauardini  (Thomse)  Geometria 
speculativa,  cum  Tractatu  de  Quadratura  Circuli  bene  revisa  a 
Petro  Sanchez  Ciruelo,  SCARCE,  folio.  Parisiis,  J.  Petit,  1511. 

'  In  this  work  we  find  the  polygones  etoiles,  see  Chasles  (Aperpu,, 
pp.  480,  487,  521,  523,  &c.)  on  the  merit  of  the  discoveries  of 
this  English  mathematician,  who  was  Archbishop  of  Canterbury 
in  the  xivth  Century  (tempore  Edward  III.  A.D.  1349) ;  and 
who  applied  geometry  to  theology.  M.  Chasles  says  that  the 
present  work  of  Bradwardine  contains  "  Une  theorie  nouvelle  qui 
doit  faire  honneur  au  xive  Siecle." ' 

The  titles  do  not  make  it  quite  sure  that  Bradwardine  is  the 
quadrator ;  it  may  be  Peter  Sanchez  after  all. 

Nouvelle  theorie  des  paralleles.  Par  Adolphe  Kircher  [so  signed 
at  the  end  of  the  appendix].  Paris,  1803,  8vo. 

An  alleged  emendation  of  Legendre.  The  author  refers  to 
attempts  by  Hoffman,  1801,  by  Hauff,  1799,  and  to  a  work  of 
Karsten,  or  at  least  a  theory  of  Karsten,  contained  in  '  Tentamen 
novse  parallelarum  theorise  notione  situs  fundatae ;  auctore  Gr.  C. 


ROSSI— W.   SPENCE— PANICS.  137 

Scliwal,  Stuttgardae,  1801,  en  8  vohimes.'  Surely  this  is  a  mis- 
print ;  eight  volumes  on  the  theory  of  parallels  ?  If  there  be 
such  a  work,  I  trust  I  and  it  may  never  meet,  though  ever  so 
far  produced. 

Soluzione  .  .  .  della  quadratura  del  Circolo.  By  Gaetano  Rossi. 
London,  1804,  8vo. 

The  three  remarkable  points  of  this  book  are,  that  the  house- 
hold of  the  Printfe  of  Wales  took  ten  copies,  Signora  Grassini 
sixteen,  and  that  the  circumference  is  3|-  diameters.  That  is, 
the  appetite  of  Grassini  for  quadrature  exceeded  that  of  the 
whole  household  (loggia)  of  the  Prince  of  Wales  in  the  ratio  in 
which  the  semi-circumference  exceeds  the  diameter.  And  these 
are  the  first  two  in  the  list  of  subscribers.  Did  the  author  see 
this  theorem  ? 

Britain  independent  of  commerce  ;  or  proofs,  deduced  from  an  in- 
vestigation into  the  true  causes  of  the  wealth  of  nations,  that  our 
riches,  prosperity,  and  power  are  derived  from  sources  inherent 
in  ourselves,  and  would  not  be  affected,  even  though  our 
commerce  were  annihilated.  By  Wm.  Spence.  4th  edition, 
1808,  8vo. 

A  patriotic  paradox,  being  in  alleviation  of  the  Commerce 
panic  which  the  measures  of  Napoleon  I. — who  felt  our  Commerce, 
while  Mr.  Spence  only  saw  it — had  awakened.  In  this  very 
month  (August,  1866),  the  Pres.  Brit.  Assoc.  has  applied  a 
similar  salve  to  the  coal  panic ;  it  is  fit  that  science,  which 
rubbed  the  sore,  should  find  a  plaster.  We  ought  to  have  an 
iron  panic  and  a  timber  panic ;  and  a  solemn  embassy  to  the 
Americans,  to  beg  them  not  to  whittle,  would  be  desirable. 
There  was  a  gold  panic  beginning,  before  the  new  fields  were 
discovered.  For  myself,  I  am  the  unknown  and  unpitied  victim 
of  a  chronic  gutta-percha  panic :  I  never  could  get  on  without 
it;  to  me,  gutta  percha  and  Eowland  Hill  are  the  great  dis- 
coveries of  our  day ;  and  not  unconnected  either,  gutta  percha 
being  to  the  submarine  post  what  Eowland  Hill  is  to  the  super- 
terrene.  I  should  be  sorry  to  lose  cow-choke — I  gave  up  trying 
to  spell  it  many  years  ago — but  if  gutta  percha  go,  I  go  too. 
I  think,  that  perhaps  when,  five  hundred  years  hence,  the  people 
say  to  the  Brit.  Assoc.  (if  it  then  exist)  « Pray,  gentlemen,  is  it 
not  time  for  the  coal  to  be  exhausted  ?  '  they  will  be  answered  out 
of  Moliere  (who  will  certainly  then  exist) :  Cela  etait  autrefois 
ainsi,  mais  nous  avons  change  taut  cela.  A  great  many  people 


138  A   BUDGET   OF   PABADOXES. 

think  that  if  the  coal  be  used  up,  it  will  be  announced  some 
unexpected  morning  by  all  the  yards  being  shut  up  and  written 
notice  outside,  '  Coal  all  gone  1 '  just  like  the  *  Please,  ma'am, 
there  ain't  no  more  sugar,'  with  which  the  maid  servant  damps 
her  mistress  just  at  breakfast- time.  But  these  persons  should 
be  informed  that  there  is  every  reason  to  think  that  there  will 
be  time,  as  the  city  gentleman  said,  to  venienti  the  occurrite 
morbo. 


An  appeal  to  the  republic  of  letters  in  behalf  of  injured  science, 
from  the  opinions  and  proceedings  of  some  modern  authors  of 
elements  of  geometry.  By  George  Douglas.  Edinburgh, 
1810,  8vo. 

Mr.  Douglas  was  the  author  of  a  very  good  set  of  mathematical 
tables,  and  of  other  works.  He  criticizes  Simson,  Playfair,  and 
others, — sometimes,  I  think,  very  justly.  There  is  a  curious 
phrase,  which  occurs  more  than  once.  When  he  wants  to  say 
that  something  or  other  was  done  before  Simson  or  another  was 
born,  he  says  '  before  he  existed,  at  least  as  an  author.'  He 
seems  to  reserve  the  possibility  of  Simson's  pre-existence,  but  at 
the  same  time  to  assume  that  he  never  wrote  anything  in  his 
previous  state.  Tell  me  that  Simson  pre-existed  in  any  other 
way  than  as  editor  of  some  pre-existent  Euclid  ?  Tell  Apella  ! 

1810.  In  this  year  Jean  Wood,  Professor  of  Mathematics  in 
the  University  of  Virginia  (Eichmond),  addressed  a  printed 
circular  to  'Dr.  Her sch el,  Astronomer,  Greenwich  Observatory.' 
No  mistake  was  more  common  than  the  natural  one  of  imagining 
that  the  Private  Astronomer  of  the  king  was  the  Astronomer 
Royal.  The  letter  was  on  the  difference  of  velocities  of  the  two 
sides  of  the  earth,  arising  from  the  composition  of  the  rotation 
and  the  orbital  motion.  The  paradox  is  a  fair  one,  and 
deserving  of  investigation ;  but,  perhaps  it  would  not  be  easy  to 
deduce  from  it  tides,  trade-winds,  aerolithes,  &c.,  as  Mr.  Wood 
thought  he  had  done  in  a  work  from  which  he  gives  an  extract, 
and  which  he  describes  as  published.  The  composition  of  rota- 
tions, &c.,  is  not  for  the  world  at  large :  the  paradox  of  the 
non-rotation  of  the  moon  about  her  axis  is  an  instance.  How 
many  persons  know  that  when  a  wheel  rolls  on  the  ground,  the 
lowest  point  is  moving  upwards,  the  highest  point  forwards,  and 
the  intermediate  points  in  all  degrees  of  betwixt  and  between  ? 
This  is  too  short  an  explanation,  with  some  good  difficulties. 


PARADOX   WITHOUT   STOPPING.  1:J9 


The  Elements  of  Geometry.     In  2  vols.     [By  the  Rev.  J.  Dobson, 
B.D.]    Cambridge,  1815.     4to. 

Of  this  unpunctuating  paradoxer  I  shall  give  an  account  in  his 
own  way :  he  would  not  stop  for  any  one ;  why  should  I  stop  for  him  ? 
It  is  worth  while  to  try  how  unpunctuated  sentences  will  read. 

The  reverend  J  Dobson  BD  late  fellow  of  saint  Johns  college 
Cambridge  was  rector  of  Brandesburton  in  Yorkshire  he  was 
seventh  wrangler  in  1798  and  died  in  1847  he  was  of  that  sort  of 
eccentricity  which  permits  account  of  his  private  life  if  we  may 
not  rather  say  that  in  such  cases  private  life  becomes  public  there 
is  a  tradition  that  he  was  called  Death  Dobson  on  account  of  his 
head  and  aspect  of  countenance  being  not  very  unlike  the 
ordinary  pictures  of  a  human  skull  his  mode  of  life  is  reported 
to  have  been  very  singular  whenever  he  visited  Cambridge  he  was 
never  known  to  go  twice  to  the  same  inn  he  never  would  sleep  at 
the  rectory  with  another  person  in  the  house  some  ancient  char- 
woman used  to  attend  to  the  house  but  never  slept  in  it  he  has 
been  known  in  the  time  of  coach  travelling  to  have  deferred  his 
return  to  Yorkshire  on  account  of  his  disinclination  to  travel 
with  a  lady  in  the  coach  he  continued  his  mathematical  studies 
until  his  death  and  till  his  executors  sold  the  type  all  his  tracts 
to  the  number  of  five  were  kept  in  type  at  the  university  press 
none  of  these  tracts  had  any  stops  except  full  stops  at  the  end  of 
paragraphs  only  neither  had  they  capitals  except  one  at  the 
beginning  of  a  paragraph  so  that  a  full  stop  was  generally 
followed  by  some  white  as  there  is  not  a  single  proper  name  in 
the  whole  of  the  book  I  have  I  am  not  able  to  say  whether  he 
would  have  used  capitals  before  proper  names  I  have  inserted 
them  as  usual  for  which  I  hope  his  spirit  will  forgive  me  if  I  be 
wrong  he  also  published  the  elements  of  geometry  in  two 
volumes  quarto  Cambridge  1815  this  book  had  also  no  stops 
except  when  a  comma  was  wanted  between  letters  as  in  the 
straight  lines  AB,  BC  I  should  also  say  that  though  the  title  is 
unpunctuated  in  the  author's  part  it  seems  the  publishers  would 
not  stand  it  in  their  imprint  this  imprint  is  punctuated  as  usual 
and  Deighton  and  Sons  to  prove  the  completeness  of  their  allegi- 
ance have  managed  that  comma  semicolon  colon  and  period 
shall  all  appear  in  it  why  could  they  not  have  contrived  interro- 
gation and  exclamation  this  is  a  good  precedent  to  establish  the 
separate  right  of  the  publisher  over  the  imprint  it  is  said  that 
only  twenty  of  the  tracts  were  printed  and  very  few  indeed  of  the 
book  on  geometry  it  is  doubtful  whether  any  were  sold  there  is  a 


140  A  BUDGET   OF  PAEADOXES. 

copy  of  the  geometry  in  the  university  library  at  Cambridge  and 
I  have  one  myself  the  matter  of  the  geometry  differs  entirely 
from  Euclid  and  is  so  fearfully  prolix  that  I  am  sure  no  mortal 
except  the  author  ever  read  it  the  man  went  on  without  stops 
and  without  stop  save  for  a  period  at  the  end  of  a  paragraph  this 
is  the  unpunctuated  account  of  the  unpunctuating  geometer 
suum  cuique  tribuito  Mrs  Thrale  would  have  been  amused  at  a 
Dobson  who  managed  to  come  to  a  full  stop  without  either  of  the 
three  warnings. 

I  do  not  find  any  difficulty  in  reading  Dobson's  geometry ;  and 
I  have  read  more  of  it  to  try  reading  without  stops  than  I  should 
have  done  had  it  been  printed  in  the  usual  way.  Those  who  dip 
into  the  middle  of  my  paragraph  may  be  surprised  for  a  moment 
to  see  that  '  on  account  of  his  disinclination  to  travel  with  a 
lady  in  the  coach  he  continued  his  mathematical  studies  until 
his  death  and  [further,  of  course]  until  his  executors  sold  the 
type.'  But  a  person  reading  straight  through  would  hardly  take 
it  so.  I  should  add  that,  in  order  to  give  a  fair  trial,  I  did  not 
compose  as  I  wrote,  but  copied  the  words  of  the  correspondent 
who  gave  me  the  facts,  so  far  as  they  went. 

Philosophic/,  Sacra,  or  the  principles  of  natural  Philosophy.  Ex- 
tracted from  Divine  Revelation.  By  the  Rev.  Samuel  Pike. 
Edited  by  the  Rev.  Samuel  Kittle.  Edinburgh,  1815,  8vo. 

This  is  a  work  of  modified  Hutchinsonianism,  which  I  have 
seen  cited  by  several.  Though  rather  dark  on  the  subject,  it 
seems  not  to  contradict  the  motion  of  the  earth,  or  the  doctrine 
of  gravitation,  Mr.  Kittle  gives  a  list  of  some  Hutchinsonians, 
— as  Bishop  Home  ;  Dr.  Stukeley ;  the  Eev.  W.  Jones,  author  of 
'  Physiological  Disquisitions ; '  Mr.  Spearman,  author  of  '  Letters 
on  the  Septuagint '  and  editor  of  Hutchinson ;  Mr.  Barker, 
author  of  '  Eeflexions  on  Learning ' ;  Dr.  Catcott,  author  of  a 
work  on  the  creation,  &c. ;  Dr.  Robertson,  author  of  a  '  Treatise 
on  the  Hebrew  Language  ; '  Dr.  Hollo  way,  author  of  '  Originals, 
Physical  and  Theological ; '  Dr.  Walter  Hodges,  author  of  a  work 
on  Elohim  ;  Lord  President  Forbes  (ob.  1747). 

The  Eev.  William  Jones,  above  mentioned,  (1726-1800),  the 
friend  and  biographer  of  Bishop  Home,  and  his  stout  defender, 
is  best  known  as  William  Jones  of  Nayland,  who  (1757)  pub- 
lished the  '  Catholic  Doctrine  of  the  Trinity ; '  he  was  also  strong 
for  the  Hutchinsonian  physical  trinity  of  fire,  light,  and  spirit. 
This  well-known  work  was  generally  recommended,  as  the  de- 
fence of  the  orthodox  system,  to  those  who  could  not  go  into  the 


TRINITARIAN   CONTROVERSY. 

learning  of  the  subject.  There  is  now  a  work  more  suited  to 
our  time :  '  The  Rock  of  Ages,'  by  the  Rev.  E.  H.  Bickersteth, 
now  published  by  the  Religious  Tract  Society,  without  date, 
answered  by  the  Rev.  Dr.  Sadler,  in  a  work  (1859)  entitled  Gloria 
Patri,  in  which,  says  Mr.  Bickersteth,  'the  author  has  not 
even  attempted  to  grapple  with  my  main  propositions.'  I  have 
read  largely  on  the  controversy,  and  I  think  I  know  what  this 
means.  Moreover,  when  I  see  the  note  '  There  are  two  other 
passages  to  which  Unitarians  sometimes  refer,  but  the  deduction 
they  draw  from  them  is,  in  each  case,  refuted  by  the  context' — 
I  think  I  see  why  the  two  texts  are  not  named.  Nevertheless, 
the  author  is  a  little  more  disposed  to  yield  to  criticism  than  his 
foregoers ;  he  does  not  insist  on  texts  and  readings  which  the 
greatest  editors  have  rejected.  And  he  writes  with  courtesy,  both 
direct  and  oblique,  towards  his  antagonists  ;  which,  on  his  side 
of  this  subject,  is  like  letting  in  fresh  air.  So  that  I  suspect  the 
two  books  will  together  make  a  tolerably  good  introduction  to 
the  subject  for  those  who  cannot  go  deep.  Mr.  Bickersteth's 
book  is  well  arranged  and  indexed,  which  is  a  point  of  superiority 
to  Jones  of  Nayland.  There  is  a  point  which  I  should  gravely 
recommend  to  writers  on  the  orthodox  side.  The  Unitarians  in 
England  have  frequently  contended  that  the  method  of  proving 
the  divinity  of  Jesus  Christ  from  the  New  Testament  would 
equally  prove  the  divinity  of  Moses.  I  have  not  fallen  in  the 
way  of  any  orthodox  answers  specially  directed  at  the  repeated 
tracts  written  by  Unitarians  in  proof  of  their  assertion.  If  there 
be  any,  they  should  be  more  known  ;  if  there  be  none,  some 
should  be  written.  Which  ever  side  may  be  right,  the  treatment 
of  this  point  would  be  indeed  coming  to  close  quarters.  The 
heterodox  assertion  was  first  supported,  it  is  said,  by  John  Bidle 
or  Biddle  (1615-1662)  of  Magdalen  College,  Oxford,  the  earliest 
of  the  English  Unitarian  writers,  previously  known  by  a  transla- 
tion of  part  of  Virgil  and  part  of  Juvenal.  But  I  cannot  find 
that  he  wrote  on  it.  It  is  the  subject  of  '  aipsa-swu  avaaracris^  or  a 
new  way  of  deciding  old  controversies.  By  Basanistes.  Third 
edition,  enlarged,'  London,  1815,  8vo.  It  is  the  appendix  to  the 
amusing,  'Six  more  letters  to  Grranville  Sharp,  Esq.,  .  .  .  By 
Gregory  Blunt,  Esq.'  London,  8vo.,  1803.  This  much  I  can 
confidently  say,  that  the  study  of  these  tracts  would  prevent 
orthodox  writers  from  some  curious  slips,  which  are  slips  obvious 
to  all  sides  of  opinion.  The  lower  defenders  of  orthodoxy  fre- 
quently vex  the  spirits  of  the  higher  ones. 

Since  writing  the  above  I  have  procured  Dr.  Sadler's  answer. 


142  A  BUDGET  OF  PARADOXES. 

I  thought  I  knew  what  the  challenger  meant  when  he  said  the 
respondent  had  not  grappled  with  his  main  propositions.  I 
should  say  that  he  is  clung  on  to  from  beginning  to  end.  But 
perhaps  Mr.  B.  has  his  own  meaning  of  logical  terms,  such  as 
proposition :  he  certainly  has  his  own  meaning  of  cumulative. 
He  says  his  evidence  is  cumulative ;  not  a  catena,  the  strength  of 
which  is  in  its  weakest  part,  but  distinct  and  independent  lines, 
each  of  which  corroborates  the  other.  This  is  the  very  opposite 
of  cumulative :  it  is  distributive.  When  different  arguments  are 
each  necessary  to  a  conclusion,  the  evidence  is  cumulative ;  when 
any  one  will  do,  even  though  they  strengthen  each  other,  it  is 
distributive.  The  word  cumulative  is  a  synonym  of  the  law  word 
constructive ;  a  whole  which  will  do  made  out  of  parts  which 
separately  will  not.  Lord  Strafford  opens  his  defence  with  the 
use  of  both  words  :  '  They  have  invented  a  kind  of  accumulated 
or  constructive  evidence ;  by  which  many  actions,  either  totally 
innocent  in  themselves,  or  criminal  in  a  much  inferior  degree, 
shall,  when  united,  amount  to  treason.'  The  conclusion  is,  that 
Mr.  B.  is  a  Cambridge  man  ;  the  Oxford  men  do  not  confuse  the 
elementary  terms  of  logic.  0  dear  old  Cambridge !  when  the 
New  Zealander  comes  let  him  find  among  the  relics  of  your  later 
sons  some  proof  of  attention  to  the  elementary  laws  of  thought. 
A  little-go  of  logic,  please ! 

Mr.  B.,  though  apparently  not  a  Hutchinsonian,  has  a  nibble 
at  a  physical  Trinity.  *  If,  as  we  gaze  on  the  sun  shining  in  the 
firmament,  we  see  any  faint  adumbration  of  the  doctrine  of  the 
Trinity  in  the  fontal  orb,  the  light  ever  generated,  and  the  heat 
proceeding  from  the  sun  and  its  beams — threefold  and  yet  one, 
the  sun,  its  light,  and  its  heat, — that  luminous  globe,  and  the 
radiance  ever  flowing  from  it,  are  both  evident  to  the  eye ;  but  the 
vital  warmth  is  felt,  not  seen,  and  is  only  manifested  in  the  life 
it  transfuses  through  creation.  The  proof  of  its  real  existence  is 
self-demonstrating.' 

We  shall  see  how  Kevilo1  illustrates  orthodoxy  by  mathematics. 
It  was  my  duty  to  have  found  one  of  the  many  illustrations  from 
physics ;  but  perhaps  I  should  have  forgotten  it  if  this  instance 
had  not  come  in  my  way.  It  is  very  bad  physics.  The  sun, 
apart  from  its  light,  evident  to  the  eye  !  Heat  more  self-demon- 
strating than  light,  because  felt !  Heat  only  manifested  by  the 
life  it  diffuses !  Light  implied  not  necessary  to  life !  But  the 
theology  is  worse  than  Sabellianism.  To  adumbrate — i.e.  make 

1  The  name  assumed  by  a  "writer  who  professed  to  give  a  mathematical  explanation 
of  the  Trinity,  see  farther  on. — (Ed.) 


TRINITARIAN   CONTROVERSY— SIR   RICHARD   PHILLIPS.      143 

a  picture  of — the  orthodox  doctrine,  the  sun  must  be  heavenly 
body,  the  light  heavenly  body,  the  heat  heavenly  body :  and 
yet,  not  three  heavenly  bodies,  but  one  heavenly  body.  The 
truth  is,  that  this  illustration  and  many  others  most  strik- 
ingly illustrate  the  Trinity  of  fundamental  doctrine  held  by  the 
Unitarians,  in  all  its  differences  from  the  Trinity  of  persons  held 
by  the  Orthodox.  Be  right  which  may,  the  right  or  wrong  of 
the  Unitarians  shines  out  in  the  comparison.  Dr.  Sadler  confirms 
me — by  which  I  mean  that  I  wrote  the  above  before  I  saw  what 
he  says — in  the  following  words  :  '  The  sun  is  one  object  with  two 
properties,  and  these  properties  have  a  parallel  not  in  the  second 
and  third  persons  of  the  Trinity,  but  in  the  attributes  of  Deity.' 

The  letting  light  alone,  as  self-evident,  and  making  heat  self- 
demonstrating,  because  felt — i.e.  perceptible  now  and  then — has 
the  character  of  the  Irishman's  astronomy  : — 

Long  life  to  the  moon,  for  a  dear  noble  cratur, 
Which  serves  us  for  lamplight  all  night  in  the  dark, 
While  the  sun  only  shines  in  the  day,  which,  by  natur, 
Wants  no  light  at  all,  as  ye  all  may  remark. 

Sir  Richard  Phillips  (born  1768)  was  conspicuous  in  1793, 
when  he  was  sentenced  to  a  year's  imprisonment  for  selling 
Paine's  '  Eights  of  Man ; '  and  again  when,  in  1 807,  he  was 
knighted  as  Sheriff  of  London.  As  a  bookseller,  he  was  able  to 
enforce  his  astronomical  opinions  in  more  ways  than  others. 
For  instance,  in  James  Mitchell's  'Dictionary  of  the  Mathe- 
matical and  Physical  Sciences,'  1823,  12mo.,  which,  though  he 
was  not  technically  a  publisher,  was  printed  for  him — a  book  I 
should  recommend  to  the  collector  of  works  of  reference — there 
is  a  temperate  description  of  his  doctrines,  which  one  may  almost 
swear  was  one  of  his  conditions  previous  to  undertaking  the  work. 
Phillips  himself  was  not  only  an  anti-Newtonian,  but  carried  to  a 
fearful  excess  the  notion  that  statesmen  and  Newtonians  were 
in  league  to  deceive  the  world.  He  saw  this  plot  in  Mrs.  Airy's 
pension,  and  in  Mrs.  Somerville's.  In  1836,  he  did  me  the 
honour  to  attempt  my  conversion.  In  his  first  letter  he  says  : — 

Sir  Richard  Phillips  has  an  inveterate  abhorrence  of  all  the  pre- 
tended wisdom  of  philosophy  derived  from  the  monks  and  doctors  of 
the  middle  ages,  and  not  less  of  those  of  higher  name  who  merely 
sought  to  make  the  monkish  philosophy  more  plausible,  or  so  to  dis- 
guise it  as  to  mystify  the  mob  of  small  thinkers. 

So  little  did  his  writings  show  any  knowledge  of  antiquity, 
that  I  strongly  suspect,  if  required  to  name  one  of  the  monkish 


144  A  BUDGET  OF  PAKADOXES. 

doctors,  he  would  have  answered — Aristotle.  These  schoolmen, 
and  the  '  philosophical  trinity  of  gravitating  force,  projectile 
force,  and  void  space,'  were  the  bogies  of  his  life. 

I  think  he  began  to  publish  speculations  in  the  Monthly 
Magazine  (of  which  he  was  editor)  in  July  1817  :  these  he 
republished  separately  in  1818.  In  the  Preface,  perhaps  judging 
the  feelings  of  others  by  his  own,  he  says  that  he  '  fully  expects 
to  be  vilified,  reviled,  and  anathematized,  for  many  years  to 
come.'  Poor  man!  he  was  let  alone.  He  appeals  with  con^ 
fidence  to  the  '  impartial  decision  of  posterity ; '  but  posterity 
does  not  appoint  a  hearing  for  one  per  cent,  of  the  appeals  which 
are  made ;  and  it  is  much  to  be  feared  that  an  article  in  such  a 
work  of  reference  as  this  will  furnish  nearly  all  her  materials  fifty 
years  hence.  The  following,  addressed  to  M.  Arago,  in  1835, 
will  give  posterity  as  good  a  notion  as  she  will  probably  need : — 

Even  the  present  year  has  afforded  EVER-MEMORABLE  examples, 
paralleled  only  by  that  of  the  Romish  Conclave  which  persecuted 
Galileo.  Policy  has  adopted  that  maxim  of  Machiavel  which  teaches 
that  it  is  more  prudent  to  reward  partisans  than  to  persecute  opponents. 
Hence,  a  bigotted  party  had  influence  enough  with  the  late  short-lived 
administration  [I  think  lie  is  wrong  as  to  the  administration]  of 
Wellington,  Peel,  &c.,  to  confer  munificent  royal  pensions  on  three 
writers  whose  sole  distinction  was  their  advocacy  of  the  Newtonian 
philosophy.  A  Cambridge  professor  last  year  published  an  elaborate 
volume  in  illustration  of  Gravitation,  and  on  him  has  been  conferred  a 
pension  of  300Z.  per  annum.  A  lady  has  written  a  light  popular  view 
of  the  Newtonian  Dogmas,  and  she  has  been  complimented  by  a  pension 
of  200Z.  per  annum.  And  another  writer,  who  has  recently  published 
a  volume  to  prove  that  the  only  true  philosophy  is  that  of  Moses,  has 
been  endowed  with  a  pension  of  2007.  per  annum.  Neither  of  them 
were  needy  persons,  and  the  political  and  ecclesiastical  bearing  of  the 
whole  was  indicated  by  another  pension  of  300Z.  bestowed  on  a  political 
•writer,  the  advocate  of  all  abuses  and  prejudices.  Whether  the  con- 
duct of  the  Romish.  Conclave  was  more  base  for  visiting  with  legal 
penalties  the  promulgation  of  the  doctrines  that  the  Earth  turns  on  its 
axis  and  revolves  around  the  Sun ;  or  that  of  the  British  Court,  for  its 
craft  in  conferring  pensions  on  the  opponents  of  the  plain  corollary, 
that  all  the  motions  on  the  Earth  are  '  part  and  parcel '  of  these  great 
motions,  and  those  again  and  all  like  them  consecutive  displays  of 
still  greater  motions  in  equality  of  action  and  reaction,  is  A  QUESTION 
which  must  be  reserved  for  the  casuists  of  other  generations.  .  .  I 
cannot  expect  that  on  a  sudden  you  and  your  friends  will  come  to  my 
conclusion,  that  the  present  philosophy  of  the  Schools  and  Univer- 
sities of  Europe,  based  on  faith  in  witchcraft,  magic,  &c.,  is  a  system 
of  execrable  nonsense,  by  which  quacks  live  on  the  faith  of  fools  ;  but  I 
desire  a  free  and  fair  examination  of  my  Aphorisms,  and  if  a  few  are 


PHILLIPS— WOOD- SATIRICAL  PARADOX.  145 

admitted  to  be  true,  merely  as  courteous  concessions  to  arithmetic,  my 
purpose  will  be  effected,  for  men  will  thus  be  led  to  think ;  and  if  they 
think,  then  the  fabric  of  false  assumptions,  and  degrading  superstitions 
will  soon  tumble  in  ruins. 

This  for  posterity.  For  the  present  time  I  ground  the  fame  of 
Sir  Pt.  Phillips  on  his  having  squared  the  circle  without  knowing 
it,  or  intending  to  do  it.  '  •  In  the  Protest  presently  noted  he 
discovered  that  '  the  force  taken  as  1  is  equal  to  the  sum  of  all 
its  fractions  ....  thus  1  =  i  +  §-  +  TV  +  aV?  &c-j  carried  to  in- 
finity.' This  the  mathematician  instantly  sees  is  equivalent  to 
the  theorem  that  the  circumference  of  any  circle  is  double  of  the 
diagonal  of  the  cube  on  its  diameter. 

I  have  examined  the  following  works  of  Sir  E.  Phillips,  and 
heard  of  many  others  : — 

Essays  on  the  proximate  mechanical  causes  of  the  general  phe- 
nomena of  the  Universe,  1818,  12mo. 

Protest  against  the  prevailing  principles  of  natural  philosophy, 
with  the  development  of  a  common  sense  system  (no  date, 
8vo.  pp.  16). 

Four  dialogues  between  an  Oxford  Tutor  and  a  disciple  of  the 
common-sense  philosophy,  relative  to  the  proximate  causes  of 
material  phenomena.  8vo.  1824. 

A  century  of  original  aphorisms  on  the  proximate  causes  of  the 
phenomena  of  nature,  1835,  12mo. 

Sir  Richard  Phillips  had  four  valuable  qualities ;  honesty, 
zeal,  ability,  and  courage.  He  applied  them  all  to  teaching 
matters  about  which  he  knew  nothing ;  and  gained  himself  an 
uncomfortable  life  and  a  ridiculous  memory. 

Astronomy  made  plain ;  or  only  way  the  true  perpendicular  dis- 
tance of  the  Sun,  Moon,  or  Stars,  from  this  earth,  can  be 
obtained.  By  Wm.  Wood.  Chatham,  1819,  12mo. 

If  this  theory  be  true,  it  will  follow,  of  course,  that  this  earth  is  the 
only  one  God  made,  and  that  it  does  not  whirl  round  the  sun,  but  vice 
versa,  the  sun  round  it. 

Historic  doubts  relative  to  Napoleon  Buonaparte.     London,  ]  819, 

8vo. 

This  tract  has  since  been  acknowledged  by  Archbishop 
"\Vhately  and  reprinted.  It  is  certainly  a  paradox :  but  differs 
from  most  of  those  in  my  list  as  being  a  joke,  and  a  satire  upon 
the  reasoning  of  those  who  cannot  receive  narrative,  no  matter 

L 


146  A   BUDGET   OF  PAKADOXES. 

what  the  evidence,  which  is  to  them  utterly  improbable  a  priori. 
But  had  it  been  serious  earnest,  it  would  not  have  been  so  absurd 
as  many  of  those  which  I  have  brought  forward.  The  next  on 
the  list  is  not  a  joke. 

The  idea  of  the  satire  is  not  new.  Dr.  King,  in  the  dispute 
on  the  genuineness  of  Phalaris,  proved  with  humour  that  Bentley 
did  not  write  his  own  dissertation.  An  attempt  has  lately  been 
made,  for  the  honour  of  Moses,  to  prove,  without  humour,  that 
Bishop  Colenso  did  not  write  his  own  book.  This  is  intolerable  : 
anybody  who  tries  to  use  such  a  weapon  without  banter,  plenty 
and  good,  and  of  form  suited  to  the  subject,  should  get  the 
drubbing  which  the  poor  man  got  in  the  Oriental  tale  for  striking 
the  dervishes  with  the  wrong  hand. 

The  excellent  and  distinguished  author  of  this  tract  has  ceased 
to  live.  I  call  him  the  Paley  of  our  day :  with  more  learning, 
and  more  purpose  than  his  predecessor ;  but  perhaps  they  might 
have  changed  places  if  they  had  changed  centuries.  The  clever 
satire  above  named  is  not  the  only  work  which  he  published 
without  his  name.  The  following  was  attributed  to  him,  I 
believe  rightly :  '  Considerations  on  the  Law  of  Libel,  as  relating 
to  Publications  on  the  subject  of  Eeligion,  by  John  Search.' 
London,  1833,  8vo.  This  tract  excited  little  attention:  for  those 
who  should  have  answered,  could  not.  Moreover,  it  wanted  a 
prosecution  to  call  attention  to  it :  the  fear  of  calling  such  atten- 
tion may  have  prevented  prosecutions.  Those  who  have  read  it 
will  have  seen  why. 

The  theological  review  elsewhere  mentioned  attributes  the 
pamphlet  of  John  Search  on  blasphemous  libel  to  Lord  Brougham. 
This  is  quite  absurd  :  the  writer  states  points  of  law  on  credence 
where  the  judge  must  have  spoken  with  authority.  Besides  which, 
a  hundred  points  of  style  are  decisive  between  the  two.  I  think 
any  one  who  knows  Whately's  writings  will  soon  arrive  at  my 
conclusion.  Lord  Brougham  himself  informs  me  that  he  has  no 
knowledge  whatever  of  the  pamphlet. 

It  is  stated  in  Notes  and  Queries  (3  S.  xi.  511)  that  Search 
was  answered  by  the  Bishop  of  P'erns  as  S.N.,  with  a  rejoinder  by 
Blanco  White.  These  circumstances  increase  the  probability  that 
Whately  was  written  against  and  for. 

Voltaire  Chretien ;  preuves  tirees  de  ses  ouvrages.     Paris,  1820, 
12mo. 

If  Voltaire  have  not  succeeded  in  proving  himself  a  strong 
theist  and  a  strong  anti-revelationist,  who  is  to  succeed  in  proving 


THE  WORD  CHRISTIAN.  147 

himself  one  thing  or  the  other  in  any  matter  whatsoever  ?  By 
occasional  confusion  between  theism  and  Christianity ;  by  taking 
advantage  of  the  formal  phrases  of  adhesion  to  the  Eoman 
Church,  which  very  often  occur,  and  are  often  the  happiest  bits 
of  irony  in  an  ironical  production  ;  by  citations  of  his  morality, 
which  is  decidedly  Christian,  though  often  attributed  to  Brah- 
mins ;  and  so  on — the  author  makes  a  fair  case  for  his  paradox, 
in  the  eyes  of  those  who  know  no  more  than  he  tells  them.  If 
he  had  said  that  Voltaire  was  a  better  Christian  than  himself 
knew  of,  towards  all  mankind  except  men  of  letters,  I  for  one 
should  have  agreed  with  him. 

Christian  !  the  word  has  degenerated  into  a  synonym  of  man, 
in  what  are  called  Christian  countries.  So  we  have  the  porrot 
who  '  swore  for  all  the  world  like  a  Christian,'  and  the  two  dogs 
who  '  hated  each  other  just  like  Christians.'  When  the  Irish 
duellist  of  the  last  century,  whose  name  may  be  spared  in 
consideration  of  its  historic  fame  and  the  worthy  people  who 
bear  it,  was  (June  12,  1786)  about  to  take  the  consequence  of 
his  last  brutal  murder,  the  rope  broke,  and  the  criminal  got  up, 

and  exclaimed,  l  By Mr.  Sheriff,  you  ought  to  be  ashamed 

of  yourself !  this  rope  is  not  strong  enough  to  hang  a  dog,  far 
less  a  Christian  ! '  But  such  things  as  this  are  far  from  the  worst 
depravations.  As  to  a  word  so  defiled  by  usage,  it  is  well  to 
know  that  there  is  a  way  of  escape  from  it,  without  renouncing 
the  New  Testament.  I  suppose  any  one  may  assume  for  himself 
what  I  have  sometimes  heard  contended  for,  that  no  New  Testa- 
ment word  is  to  be  used  in  religion  in  any  sense  except  that  of 
the  New  Testament.  This  granted,  the  question  is  settled. 
The  word  Christian,  which  occurs  three  times,  is  never  recog- 
nised as  anything  but  a  term  of  contempt  from  those  without 
the  pale  to  those  within.  Thus,  Herod  Agrippa,  who  was  deep  in 
Jewish  literature,  and  a  correspondent  of  Josephus,  says  to  Paul, 
(Acts  xxvi.  28)  '  Almost  thou  persuadest  me  to  be  (what  I  and 
other  followers  of  the  state  religion  depise  under  the  name) 
a  Christian.'  Again,- ( Acts  xi.  26)  'The  disciples  (as  they  called 
themselves)  were  called  (by  the  surrounding  heathens)  Christians 
first  in  Antioch.'  Thirdly,  (1  Peter  iv.  16)  'Let  none  of  you 
suffer  as  a  murderer.  .  .  .  But  if  as  a  Christian  (as  the  heathen 
call  it  by  whom  the  suffering  comes),  let  him  not  be  ashamed.' 
That  is  to  say,  no  disciple  ever  called  himself  a  Christian,  or 
applied  the  name,  as  from  himself,  to  another  disciple,  from  one 
end  of  the  New  Testament  to  the  other ;  and  no  disciple  need 

L    2 


148  A  BUDGET  OF  PARADOXES. 

apply  that  name  to  himself  in  our  day,  if  he  dislike  the  associa- 
tions with  which  the  conduct  of  Christians  has  clothed  it. 

Address  of  M.  Hoene  Wronski  to  the  British  Board  of  Longitude, 

upon  the  actual  state  of  the  mathematics,  their  reform,  and 

upon  the  new  celestial  mechanics,  giving  the  definitive  solution 

of  the  problem  of  longitude.     London,  1820,  8vo. 

M.  Wronski  was  the  author  of  seven  quartos  on  mathematics, 

showing  very  great  power  of  generalization.     He  was  also  deep  in 

the   transcendental   philosophy,   and   had   the   Absolute   at   his 

fingers'  ends.      All  this  knowledge  was   rendered  useless  by  a 

persuasion  that  he  had  greatly  advanced  beyond  the  whole  world, 

with  many  hints  that  the  Absolute  would  not  be  forthcoming, 

unless   prepaid.     He   was   a  man  of  the   widest  extremes.     At 

one  time  he  desired  people  to  see  all  possible  mathematics  in 

Faj= A0O0  +  A1fl1  +  A2O2  +  A3H3  +  &c, 

which  he  did  not  explain,  though  there  is  meaning  to  it  in  the 
quartos.  At  another  time  he  was  proposing  the  general  solution 
of  the  fifth  degree  by  help  of  625  independent  equations  of  one 
form  and  125  of  another.  The  first  separate  memoir  from  any 
Transactions  that  t  ever  possessed  was  given  to  me  when  at 
Cambridge;  the  refutation  (1819)  of  this  asserted  solution, 
presented  to  the  Academy  of  Lisbon  by  Evangelista  Torriano. 
I  cannot  say  I  read  it.  The  tract  above  is  an  attack  on  modern 
mathematicians  in  general,  and  on  the  Board  of  Longitude,  and 
Dr.  Young. 

1820.  In  this  year  died  Dr.  Isaac  Milner,  President  of  Queens' 
College,  Cambridge,  one  of  the  class  of  rational  paradoxers. 
Under  this  name  I  include  all  who,  in  private  life,  and  in  matters 
which  concern  themselves,  take  their  own  course,  and  suit  their 
own  notions,  no  matter  what  other  people  may  think  of  them. 
These  men  will  put  things  to  uses  they  were  never  intended  for, 
to  the  great  distress  and  disgust  of  their  gregarious  friends.  I 
am  one  of  the  class,  and  I  could  write  a  little  book  of  cases  in 
which  I  have  incurred  absolute  reproach  for  not  '  doing  as  other 
people  do.'  I  will  name  two  of  my  atrocities  :  I  took  one  of 
those  butter-dishes  which  have  for  a  top  a  dome  with  holes  in 
it,  which  is  turned  inward,  out  of  reach  of  accident,  when  not  in 
use.  Turning  the  dome  inwards,  I  filled  the  dish  with  water, 
and  put  a  sponge  in  the  dome :  the  holes  let  it  fill  with  water, 
and  I  had  a  penwiper,  always  moist,  and  worth  its  price  five 
times  over.  '  Why !  what  do  you  mean  ?  It  was  made  to  hold 


MILNER'S   LAMP.  149 

butter.  You  are  always  at  some  queer  thing  or  other ! '  I 
bought  a  leaden  comb,  intended  to  dye  the  hair,  it  being  sup- 
posed that  the  application  of  lead  will  have  this  effect.  I  did 
not  try :  but  I  divided  the  comb  into  two,  separating  the  part 
of  closed  prongs  from  the  other ;  and  thus  I  had  two  ruling 
machines.  The  lead  marks  paper,  and  by  drawing  the  end  of 
one  of  the  machines  along  a  ruler,  I  could  rule  twenty  lines  at 
a  time,  quite  fit  to  write  on.  I  thought  I  should  have  killed  a 
friend  to  whom  I  explained  it :  he  could  not  for  the  life  of  him 
understand  how  leaden  lines  on  paper  would  dye  the  hair. 

But  Dr.  Milner  went  beyond  me.  He  wanted  a  seat  suited  to 
his  shape,  and  he  defied  opinion  to  a  fearful  point.  He  spread  a 
thick  block  of  putty  over  a  wooden  chair  and  sat  in  it  until  it 
had  taken  a  ceroplast  copy  of  the  proper  seat.  This  he  gave  to 
a  carpenter  to  be  imitated  in  wood.  One  of  the  few  now  living 
who  knew  him — my  friend,  General  Perronet  Thompson — 
answers  for  the  wood,  which  was  shown  him  by  Milner  himself  ; 
but  he  does  not  vouch  for  the  material  being  putty,  which  was 
in  the  story  told  me  at  Cambridge ;  William  Frend  also  re- 
membered it.  Perhaps  the  Doctor  took  off  his  great  seal  in 
green  wax,  like  the  Crown ;  but  some  soft  material  he  certainly 
adopted ;  and  very  comfortable  he  found  the  wooden  copy. 

The  same  gentleman  vouches  for  Milner's  lamp :  but  this  had 
visible  science  in  it ;  the  vulgar  see 
no  science  in  the  construction  of  the 
chair.  A  hollow  semi-cylinder,  but 
not  with  a  circular  curve,  revolved  on 
pivots.  The  curve  was  calculated  on 
the  law  that,  whatever  quantity  of  oil 
might  be  in  the  lamp,  the  position  of 
equilibrium  just  brought  the  oil  up  to 
the  edge  of  the  cylinder,  at  which  a 
bit  of  wick  was  placed.  As  the  wick 
exhausted  the  oil,  the  cylinder  slowly 
revolved  about  the  pivots  so  as  to 
keep  the  oil  always  touching  the  wick. 

Great  discoveries  are  always  laughed  at :  but  it  is  very  often 
not  the  laugh  of  incredulity  ;  it  is  a  mode  of  distorting  the  sense 
of  inferiority  into  a  sense  of  superiority,  or  a  mimicry  of  supe- 
riority interposed  between  the  laugher  and  his  feeling  of  in- 
feriority. Two  persons  in  conversation  agreed  that  it  was  often 


150  A  BUDGKET  OF  PARADOXES. 

a  nuisance  not  to  be  able  to  lay  hands  on  a  bit  of  paper  to  mark 
the  place  in  a  book,  every  bit  of  paper  on  the  table  was  sure  to 
contain  something  not  to  be  spared.  I  very  quietly  said  that  I 
always  had  a  stock  of  bookmarkers  ready  cut,  with  a  proper  place 
for  them  :  my  readers  owe  many  of  my  anecdotes  to  this  absurd 
practice.  My  two  colloquials  burst  into  a  fit  of  laughter  ;  about 
what  ?  Incredulity  was  out  of  the  question  ;  and  there  could  be 
nothing  foolish  in  my  taking  measures  to  avoid  what  they  knew 
was  an  inconvenience.  I  was  in  this  matter  obviously  their 
superior,  and  so  they  laughed  at  me.  Much  more  candid  was 
the  Eoyal  Duke  of  the  last  century,  who  was  noted  for  slow  ideas. 
'  The  rain  comes  into  my  mouth,'  said  he,  while  riding.  '  Had 
not  your  Royal  Highness  better  shut  your  mouth  ?  '  said  the 
equerry.  The  Prince  did  so,  and  ought,  by  rule,  to  have  laughed 
heartily  at  his  adviser  ;  instead  of  this,  he  said  quietly,  '  It 
doesn't  come  in  now.' 

De  Attentionis  mensura  causisque  primariis.     By  J.  F.  Herbart. 
Koenigsberg,  1822,  4to. 

This  celebrated  philosopher  maintained  that  mathematics 
ought  to  be  applied  to  psychology,  in  a  separate  tract,  published 
also  in  1822  :  the  one  above  seems,  therefore,  to  be  his  challenge 
on  the  subject.  It  is  on  attention,  and  I  think  it  will  hardly 
support  Herbart's  thesis.  As  a  specimen  of  his  formula,  let  t  be 
the  time  elapsed  since  the  consideration  began,  /3  the  whole 
perceptive  intensity  of  the  individual,  (f>  the  whole  of  his  mental 
force,  and  z  the  force  given  to  a  notion  by  attention  during  the 
time  t.  Then, 


Now  for  a  test.  There  is  a  jactura,  v,  the  meaning  of  which  I 
do  not  comprehend.  If  there  be  anything  in  it,  my  mathe- 
matical readers  ought  to  interpret  it  from  the  formula 


1-/3 

and  to  this  task  I  leave  them,  wishing  them  better  luck  than 
mine.  The  time  may  come  when  other  manifestations  of  mind, 
besides  belief,  shall  be  submitted  to  calculation  :  at  that  time, 
should  it  arrive,  a  final  decision  may  be  passed  upon  Herbart. 


THE   WHIZGIG— MYTHOLOGICAL  ASTRONOMY.  151 


The  theory  of  the  Whizgtg  considered  ;  in  as  much  as  it  mechani- 
cally exemplifies  the  three  working  properties  of  nature  ;  which 
are  now  set  forth  under  the  guise  of  this  toy,  for  children  of  all 
ages.  London,  1822,  12mo.  (pp.  24,  B.  McMillan,  Bow  Street, 
Covent  Garden.) 

The  toy  called  the  whizgig  will  be  remembered  by  many.  The 
writer  is  a  follower  of  Jacob  Behmen,  William  Law,  Richard 
Clarke,  and  Eugenius  Philaleth.es.  Jacob  Behmen  first  an- 
nounced the  three  working  properties  of  nature,  which  Newton 
stole,  as  described  in  the  Gentleman's  Magazine,  July,  1782, 
p.  329.  These  laws  are  illustrated  in  the  whizgig.  There  is  the 
harsh  astringent,  attractive  compression  ;  the  bitter  compunction, 
repulsive  expansion ;  and  the  stinging  anguish,  duplex  motion. 
The  author  hints  that  he  has  written  other  works,  to  which  he 
gives  no  clue.  I  have  heard  that  Behmen  was  pillaged  by  New- 
ton, and  Swedenborg  by  Laplace,  and  Pythagoras  by  Copernicus, 
and  Epicurus  by  Dalton,  &c.  I  do  not  think  this  mention  will 
revive  Behmen ;  but  it  may  the  whizgig,  a  very  pretty  toy,  and 
philosophical  withal,  for  few  of  those  who  used  it  could  ex- 
plain it. 

A  Grammar  of  infinite  forms ;  or  the  mathematical  elements  of 
ancient  philosophy  and  mythology.  By  Wm.  Howison.  Edin- 
burgh, 1823,  8vo. 

A  curious  combination  of  geometry  and  mythology.  Perseus, 
for  instance,  is  treated  under  the  head, '  the  evolution  of  diminish- 
ing hyperbolic  branches.' 

The  Mythological  Astronomy  of  the  Ancients ;  part  the  second  : 
or  the  key  of  Urania,  the  wards  of  which  will  unlock  all  the 
mysteries  of  antiquity.  Norwich,  1823,  12mo. 

A  Companion  to  the.  Mythological  Astronomy,  &c.,  containing 
remai'ks  on  recent  publications.  .  .  Norwich,  1824,  12mo. 

A  new  Theory  of  the  Earth  and  of  planetary  motion ;  in  which  it 
is  demonstrated  that  the  Sun  is  vicegerent  of  his  own  system. 
Norwich,  1825,  12mo. 

The  analyzation  of  the  writings  of  the  Jews,  so  far  as  they  are 
found  to  have  any  connection  with  the  sublime  science  of 
astronomy.  [This  is  pp.  97-180  of  some  other  work,  being  all 
I  have  seen.] 

These  works  are  all  by  Sampson  Arnold  Mackey,  for  whom  see 
Notes  and  Queries,  1st  S.  viii.  468,  565,  ix.  89,  179.  Had  it 


J52  A   BUDGET   OF  PARADOXES. 

not  been  for  actual  quotations  given  by  one  correspondent  only 
(1st  S.  viii.  565),  that  journal  would  have  handed  him  down  as 
a  man  of  some  real  learning.  An  extraordinary  man  he  certainly 
was :  it  is  not  one  illiterate  shoemaker  in  a  thousand  who  could  work 
upon  such  a  singular  mass  of  Sanscrit  and  Greek  words,  without 
showing  evidence  of  being  able  to  read  a  line  in  any  language 
but  his  own,  or  to  spell  that  correctly.  He  was  an  uneducated 
Godfrey  Higgins.  A  few  extracts  will  put  this  in  a  strong  light : 
one  for  history  of  science,  one  for  astronomy,  and  one  for  philo- 
logy : — 
&j  v 

'  Sir  Isaac  Newton  was  of  opinion  that  "  the  atmosphere  of  the  earth 
was  the  sensory  of  God  ;  by  which  he  was  enabled  to  see  quite  round 
the  earth  : "  which  proves  that  Sir  Isaac  had  no  idea  that  God  could 
see  through  the  earth. 

Sir  Richard  [Phillips]  has  given  the  most  rational  explanation  of 
the  cause  of  the  earth's  elliptical  orbit  that  I  have  ever  seen  in  print. 
It  is  because  the  earth  presents  its  watery  hemisphere  to  the  sun  at 
one  time  and  that  of  solid  land  the  other ;  but  why  has  he  made  his 
Oxonian  astonished  at  the  coincidence  ?  It  is  what  I  taught  in  my 
attic  twelve  years  before. 

Again,  admitting  that  the  Eloim  were  powerful  and  intelligent  beings 
that  managed  these  things,  we  would  accuse  them  of  being  the  authors 
of  all  the  sufferings  of  Chrisna.  And  as  they  and  the  constellation  of 
Leo  were  below  the  horizon,  and  consequently  cut  off  from  the  end  of 
the  zodiac,  there  were  but  eleven  constellations  of  the  zodiac  to  be 
seen ;  the  three  at  the  end  were  wanted,  but  those  three  would  be 
accused  of  bringing  Chrisna  into  the  troubles  which  at  last  ended  in 
his  death.  All  this  would  be  expressed  in  the  Eastern  language  by 
saying  that  Chrisna  was  persecuted  by  those  Judoth  Isbcariotb  ! !  !  !  ! 
[the  five  notes  of  exclamation  are  the  author's].  But  the  astronomy 
of  those  distant  ages,  when  the  sun  was  at  the  south  pole  in  winter, 
would  leave  five  of  those  Decans  cut  off  from  our  view,  in  the  latitude 
of  twenty-eight  degrees;  hence  Chrisna  died  of  wounds  from  five 
Decans,  but  the  whole  five  may  be  included  in  Judoth  Ishcarioth  !  for 
the  phrase  means  the  men  that  are  wanted  at  the  extreme  parts.  Ish- 
carioth is  a  compound  of  ish,  a  man,  and  carat  wanted  or  taken  away, 
and  oth  the  plural  termination,  more  ancient  than  im. .  . ' 

I  might  show  at  length  how  Michael  is  the  sun,  and  the 
D'-ev-'l,  in  French  Di-ob-al,  also  'L-evi-ath-an — the  evi  being  the 
radical  part  both  of  devil  and  leviathan — is  the  Nile,  which  the 
sun  dried  up  for  Moses  to  pass :  a  battle  celebrated  by  Jude. 
Also  how  Moses,  the  same  name  as  Muses,  is  from  mesha,  drawn 
out  of  the  water,  '  and  hence  we  called  our  land  which  is  saved 
from  the  water  by  the  name  of  marsh.''  But  it  will  be  of  more  use 
to  collect  the  character  of  S.  A.  M.  from  such  correspondents  of 


A  TKANSCENDENTAL  PHILOSOPHER.  153 

Notes  and  Queries  as  have  written  after  superficial  examination. 
Great  astronomical  and  philological  attainments  ;  much  ability 
and  learning;  had  evidently  read  and  studied  deeply;  remark- 
able for  the  originality  of  his  views  upon  the  very  abstruse 
subject  of  mythological  astronomy,  in  which  he  exhibited  great 
sagacity.  Certainly  his  views  were  original ;  but  their  sagacity, 
if  it  be  allowable  to  copy  his  own  mode  of  etymologizing,  is  of  an 
ori-gin-ale  cast,  resembling  that  of  a  person  who  puts  to  his 
mouth  liquors  both  distilled  and  fermented. 

Principles  of  the  Kantesian,  or  transcendental  philosophy.      By 
Thomas  Wirgman.     London,  1824,  8vo. 

Mr.  Wirgman's  mind  was  somewhat  attuned  to  psychology; 
but  he  was  cracky  and  vagarious.  He  had  been  a  fashionable 
jeweller  in  St.  James's  Street,  no  doubt  the  son  or  grandson  of 
Wirgman  at  'the  well-known  toy-shop  in  St.  James's  Street,' 
where  Sam  Johnson  smartened  himself  with  silver  buckles. 
(Boswell,  aet.  69).  He  would  not  have  the  ridiculous  large  ones 
in  fashion  ;  and  he  would  give  no  more  than  a  guinea  a  pair ; 
such,  says  Boswell,  in  Italics,  were  the  principles  of  the  business : 
and  I  think  this  may  be  the  first  place  in  which  the  philo- 
sophical word  was  brought  down  from  heaven  to  mix  with  men. 
However  this  may  be,  my  Wirgman  sold  snuff-boxes,  among 
other  things,  and  fifty  years  ago  a  fashionable  snuff-boxer  would 
be  under  inducement,  if  not  positively  obliged,  to  have  a  stock 
with  very  objectionable  pictures.  So  it  happened  that  Wirgman 
— by  reason  of  a  trifle  too  much  candour — came  under  the  notice 
of  the  Suppression  Society,  and  ran  considerable  risk.  Mr. 
Brougham  was  his  counsel ;  and  managed  to  get  him  acquitted. 
Years  and  years  after  this,  when  Mr.  Brougham  was  deep  in  the 
formation  of  the  London  University  (now  University  College), 
Mr.  Wirgman  called  on  him.  '  What  now  ?  '  said  Mr.  B.  with  his 
most  sarcastic  look — a  very  perfect  thing  of  its  kind — 'you're 
in  a  scrape  again,  I  suppose  ! '  '  No  !  indeed  ! '  said  W., '  my  present 
object  is  to  ask  your  interest  for  the  chair  of  Moral  Philosophy 
in  the  new  University  I '  He  had  taken  up  Kant ! 

Mr.  Wirgman,  an  itinerant  paradoxer,  called  on  me  in  1831 :  he 
came  to  convert  me.  '  I  assure  you,'  said  he,  '  I  am  nothing  but 
an  old  brute  of  a  jeweller  ; '  and  his  eye  and  manner  were  of  the 
extreme  of  jocosity,  as  good  in  their  way,  as  the  satire  of  his 
former  counsel.  I  mention  him  as  one  of  that  class  who  go  away 
quite  satisfied  that  they  have  wrought  conviction.  '  Now,'  said  he, 


154  A  BUDGET  OF  PABADOXES. 

'  I'll  make  it  clear  to  you !  Suppose  a  number  of  gold-fishes  in  a 
glass  bowl — you  understand  ?  Well !  I  come  with  my  cigar, 
and  go  puff,  puff,  puff,  over  the  bowl,  until  there  is  a  little  cloud 
of  smoke  :  now,  tell  me,  what  will  the  gold-fishes  say  to  that  ? ' 
'  I  should  imagine,'  said  I,  '  that  they  would  not  know  what  to  make 
of  it.'  '  By  Jove  !  you're  a  Kantian  ; '  said  he,  and  with  this  and 
the  like,  he  left  me,  vowing  that  it  was  delightful  to  talk  to  so 
intelligent  a  person.  The  greatest  compliment  Wirgman  ever 
received  was  from  James  Mill,  who  used  to  say  he  did  not  under- 
stand Kant.  That  such  a  man  as  Mill  should  think  this  worth 
saying  is  a  feather  in  the  cap  of  the  jocose  jeweller. 

Some  of  my  readers  will  stare  at  my  supposing  that  Boswell 
may  have  been  the  first  down-bringer  of  the  word  principles  into 
common  life ;  the  best  answer  will  be  a  prior  instance  of  the 
word  as  true  vernacular ;  it  has  never  happened  to  me  to  notice 
one.  Many  words  have  very  common  uses  which  are  not  old. 
Take  the  following  from  Nichols  (Anecd.  ix.  263) :  <  Lord 
Thurlow  presents  his  best  respects  to  Mr.  and  Mrs.  Thicknesse, 
and  assures  them  that  he  knows  of  no  cause  to  complain  of  any 
part  of  Mr.  Thicknesse's  carriage ;  least  of  all  the  circumstance  of 
sending  the  head  to  Ormond  Street.'  Surely  Mr.  T.  had  lent 
Lord  T.  a  satisfactory  carriage  with  a  moveable  head,  and  the 
above  is  a  polite  answer  to  inquiries.  Not  a  bit  of  it !  carriage 
is  here  conduct,  and  the  head  is  a  bust.  The  vehicles  of  the 
rich,  at  the  time,  were  coaches,  chariots,  chaises,  &c.,  never 
carriages,  which  were  rather  carts.  Gibbon  has  the  word  for 
baggage-waggons.  In  Jane  Austen's  novels  the  word  carriage  is 
established. 

John  Walsh,  of  Cork  (1786-1847).— This  discoverer  has  had 
the  honour  of  a  biography  from  Prof.  Boole,  who,  at  my  request, 
collected  information  about  him  on  the  scene  of  his  labours. 
It  is  in  the  Philosophical  Magazine  for  November,  1851,  and 
will,  I  hope,  be  transferred  to  some  biographical  collection  where 
it  may  find  a  larger  class  of  readers,  It  is  the  best  biography  of 
a  single  hero  of  the  kind  that  I  know.  Mr.  Walsh  introduced 
himself  to  me,  as  he  did  to  many  others,  in  the  anterowlandian 
days  of  the  Post-office ;  his  unpaid  letters  were  double,  treble, 
&c.  They  contained  his  pamphlets,  and  cost  their  weight  in 
silver  :  all  have  the  name  of  the  author,  and  all  are  in  octavo  or 
in  quarto  letter-form  :  most  are  in  four  pages,  and  all  dated  from 
Cork.  I  have  the  following  by  me  : — 


JOHN  WALSH'S  DELUSIONS.  155 


The  Geometric  Base.  1825.— The  theory  of  pl&ne  angles.  1827.— 
Three  Letters  to  Dr.  Francis  Sadleir.  1838. — The  invention  of 
polar  geometry.  By  Irelandus.  1839. — The  theory  of  partial 
functions.  Letter  to  Lord  Brougham.  1839. — On  the  invention 
of  polar  geometry.  1839. — Letter  to  the  Editor  of  the  Edin- 
burgh Review.  1840. — Irish  Manufacture.  A  new  method  of 
tangents.  1841. — The  normal  diameter  in  curves.  1843. — 
Letter  to  Sir  R.  Peel.  1845. — [Hints  that  Government  should 
compel  the  introduction  of  Walsh's  Geometry  into  Universities.] 
— Solution  of  Equations  of  the  higher  orders.  1845. 

Besides  these,  there  is  a  '  Metalogia,'  and  I  know  not  how  many 
others. 

Mr.  Boole,  who  has  taken  the  moral  and  social  features  of 
Walsh's  delusions  from  the  commiserating  point  of  view,  which 
makes  ridicule  out  of  place,  has  been  obliged  to  treat  Walsh  as 
Scott's  Alan  Fairford  treated  his  client  Peter  Peebles ;  namely, 
keep  the  scarecrow  out  of  court  while  his  case  was  argued.  My 
plan  requires  me  to  bring  him  in  :  and  when  he  comes  in  at  the 
door,  pity  and  sympathy  fly  out  at  the  window.  Let  the  reader 
remember  that  he  was  not  an  ignoramus  in  mathematics  :  he 
might  have  won  his  spurs  if  he  could  have  first  served  as  an 
esquire.  Though  so  illiterate  that  even  in  Ireland  he  never 
picked  up  anything  more  Latin  than  Irelandus,  he  was  a  very 
pretty  mathematician  spoiled  in  the  making  by  intense  self- 
opinion. 

This  is  part  of  a  private  letter  to  me  at  the  back  of  a  page  of 
print :  I  had  never  addressed  a  word  to  him  : — 

'  There  are  no  limits  in  mathematics,  and  those  that  assert  there  are, 
are  infinite  ruffians,  ignorant,  lying  blackguards.  There  is  no  dif- 
ferential calculus,  no  Taylor's  theorem,  no  calculus  of  variations,  &c. 
in  mathematics.  There  is  no  quackery  whatever  in  mathematics  ;  no 
$  equal  to  anything.  What  sheer  ignorant  blackguardism  that ! 

In  mechanics  the  parallelogram  of  forces  is  quackery,  and  is  danger- 
ous ;  for  nothing  is  at  rest,  or  in  uniform,  or  in  rectilinear  motion,  in 
the  universe.  Variable  motion  is  an  essential  property  of  matter. 
Laplace's  demonstration  of  the  parallelogram  of  forces  is  a  begging  of 
the  question ;  and  the  attempts  of  them  all  to  show  that  the  difference 
of  twenty  minutes  between  the  sidereal  and  actual  revolution  of  the 
earth  round  the  sun  arises  from  the  tugging  of  the  Sun  and  Moon  at 
the  pot-belly  of  the  earth,  without  being  sure  even  that  the  earth  has 
a  pot-belly  at  all,  is  perfect  quackery.  The  said  difference  arising 
from  and  demonstrating  the  revolution  of  the  Sun  itself  round  some 
distant  centre.' 


156  A  BUDGET  OF  PARADOXES. 

In  the  letter  to  Lord  Brougham  we  read  as  follows  : — 
'  I  ask  the  Royal  Society  of  London,  I  ask  the  Saxon  crew  of  that 
crazy  hulk,  where  is  the  dogma  of  their  philosophic  god  now  ?  .  .  . 
When  the  Royal  Society  of  London,  and  the  Academy  of  Sciences  of 
Paris,  shall  have  read  this  memorandum,  how  will  they  appear  ?  Like 
two  cur  dogs  in  the  paws  of  the  noblest  beast  of  the  forest  .  .  .  Just 
as  this  note  was  going  to  press,  a  volume  lately  published  by  you  was 
put  into  my  hands,  wherein  you  attempt  to  defend  the  fluxions  and 
Principia  of  Newton.  Man  !  what  are  you  about  ?  You  come  forward 
now  with  your  special  pleading,  and  fraught  with  national  prejudice, 
to  defend,  like  the  philosopher  Grassi,  the  persecutor  of  Galileo,  prin- 
ciples and  reasoning  which,  unless  you  are  actually  insane,  or  an 
ignorant  quack  in  mathematics,  you  know  are  mathematically  false. 
What  a  moral  lesson  this  for  the  students  of  the  University  of  London 
from  its  head  !  Man !  demonstrate  corollary  3,  in  this  note,  by  the 
lying  dogma  of  Newton,  or  turn  your  thoughts  to  something  you 
understand.' 

'WALSH  IEBLANDUS.' 

Mr.  Walsh — honour  to  his  memory — once  had  the  considera- 
tion to  save  me  postage  by  addressing  a  pamphlet  under  cover  to 
a  Member  of  Parliament,  with  an  explanatory  letter.  In  that 
letter  he  gives  a  candid  opinion  of  himself : — 

(1838.)  '  Mr.  Walsh  takes  leave  to  send  the  enclosed  corrected 
copy  to  Mr.  Hutton  as  one  of  the  Council  of  the  University  of  London, 
and  to  save  postage  for  the  Professor  of  Mathematics  there.  He  will 
find  in  it  geometry  more  deep  and  subtle,  and  at  the  same  time  more 
simple  and  elegant,  than  it  was  ever  contemplated  human  genius  could 
invent.' 

He  then  proceeds  to  set  forth  that  a  certain  '  tomfoolery 
lemma,'  with  its  '  tomfoolery '  superstructure,  *  never  had  exist- 
ence outside  the  shallow  brains  of  its  inventor,'  Euclid.  He  then 
proceeds  thus : — 

'  The  same  spirit  that  animated  those  philosophers  who  sent  Galileo 
to  the  Inquisition  animates  all  the  philosophers  of  the  present  day 
without  exception.  If  anything  can  free  them  from  the  yoke  of  error, 
it  is  the  [Walsh]  problem  of  double  tangence.  But  free  them  it  will, 
how  deeply  soever  they  may  be  sunk  into  mental  slavery — and  God 
knows  that  is  deeply  enough  ;  and  they  bear  it  with  an  admirable 
grace  ;  for  none  bear  slavery  with  a  better  grace  than  tyrants.  The 
lads  must  adopt  my  theory  ...  It  will  be  a  sad  reverse  for  all  our 
great  professors  to  be  compelled  to  become  schoolboys  in  their  gray 
years.  But  the  sore  scratch  is  to  be  compelled,  as  they  had  before 
been  compelled  one  thousand  years  ago,  to  have  recourse  to  Ireland 
for  instruction.' 


PROGRESS  OF  FREE  THOUGHT.  157 

The  following  '  Impromptu '  is  no  doubt  by  Walsh  himself:  he 
was  more  of  a  poet  than  of  an  astronomer  : — 

'  Through  ages  unfriended, 

With  sophistry  blended, 
Deep  science  in  Chaos  had  slept ; 

Its  limits  were  fettered, 

Its  voters  unlettered, 
Its  students  in  movements  but  crept. 

Till,  despite  of  great  foes, 

Great  WALSH  first  arose, 
And  with  logical  might  did  unravel 

Those  mazes  of  knowledge, 

Ne'er  known  in  a  college, 
Though  sought  for  with  unceasing  travail. 

With  cheers  we  now  hail  him, 

May  success  never  fail  him, 
In  Polar  Geometrical  mining ; 

Till  his  foes  be  as  tamed 

As  his  works  are  far-famed 
For  true  philosophic  refining.' 

Walsh's  system  is,  that  all  mathematics  and  physics  are  wrong : 
there  is  hardly  one  proposition  in  Euclid  which  is  demonstrated. 
His  example  ought  to  warn  all  who  rely  on  their  own  evidence  to 
their  own  success.  He  was  not,  properly  speaking,  insane ;  he 
only  spoke  his  mind  more  freely  than  many  others  of  his  class. 
The  poor  fellow  died  in  the  Cork  union,  during  the  famine.  He 
had  lived  a  happy  life,  contemplating  his  own  perfections,  like 
Brahma  on  the  lotos-leaf. 

The  year  1825  brings  me  to  about  the  middle  of  my  Athe- 
naeum list :  that  is,  so  far  as  mere  number  of  names  mentioned 
is  concerned.  Freedom  of  opinion,  beyond  a  doubt,  is  gaining 
ground,  for  good  or  for  evil,  according  to  what  the  speaker 
happens  to  think :  admission  of  authority  is  no  longer  made  in 
the  old  way.  If  we  take  soul-cure  and  body-cure,  divinity  and 
medicine,  it  is  manifest  that  a  change  has  come  over  us.  Time 
was  when  it  was  enough  that  dose  or  dogma  should  be  certified 
by  '  II  a  ete  ordonne,  Monsieur,  il  a  ete  ordonne,'  as  the  apothe- 
cary said  when  he  wanted  to  operate  upon  poor  de  Porceaugnac. 
Very  much  changed :  but  whether  for  good  or  for  evil  does  not 
now  matter  ;  the  question  is,  whether  contempt  of  demonstration 
such  as  our  paradoxers  show  has  augmented  with  the  rejection  of 
dogmatic  authority.  It  ought  to  be  just  the  other  way  :  for  the 


158  A  BUDGET  OF  PARADOXES. 

worship  of  reason  is  the  system  on  which,  if  we  trust  them,  the 
deniers  of  guidance  ground  their  plan  of  life.  The  following 
attempt  at  an  experiment  on  this  point  is  the  best  which  I  can 
make ;  and,  so  far  as  I  know,  the  first  that  ever  was  made. 

Say  that  my  list  of  paradoxers  divides  in  1825 :  this  of  itself 
proves  nothing,  because  so  many  of  the  earlier  books  are  lost,  or 
not  likely  to  be  come  at.  It  would  be  a  fearful  rate  of  increase 
which  would  make  the  number  of  paradoxes  since  1825  equal  to 
the  whole  number  before  that  date.  Let  us  turn  now  to  another 
collection  of  mine,  arithmetical  books,  of  which  I  have  published 
a  list.  The  two  collections  are  similarly  circumstanced  as  to 
new  and  old  books ;  the  paradoxes  had  no  care  given  to  the 
collection  of  either  ;  the  arithmetical  books  equal  care  to  both. 
The  list  of  arithmetical  books,  published  in  1847,  divides  at 
1735 ;  the  paradoxes,  up  to  1863,  divide  at  1825.  If  we  take 
the  process  which  is  most  against  the  distinction,  and  allow  every 
year  from  1847  to  1863  to  add  a  year  to  1735,  we  should  say 
that  the  arithmetical  writers  divide  at  1751.  This  rough  pro- 
cess may  serve,  with  sufficient  certainty,  to  show  that  the  pro- 
portion of  paradoxes  to  books  of  sober  demonstration  is  on  the 
increase ;  and  probably,  quite  as  much  as  the  proportion  of 
heterodoxes  to  books  of  orthodox  adherence.  So  that  divinity 
and  medicine  may  say  to  geometry,  Don't  you  sneer :  if  ration- 
alism, homoeopathy,  and  their  congeners  are  on  the  rise  among 
us,  your  enemies  are  increasing  quite  as  fast.  But  geometry 
replies — Dear  friends,  content  yourselves  with  the  rational  in- 
ference that  the  rise  of  heterodoxy  within  your  pales  is  not 
conclusive  against  you,  taken  alone  ;  for  it  rises  at  the  same 
time  within  mine.  Store  within  your  garners  the  precious 
argument  that  you  are  not  proved  wrong  by  increase  of  dissent ; 
because  there  is  increase  of  dissent  against  exact  science.  But 
do  not  therefore  even  yourselves  to  me :  remember  that  you, 
Dame  Divinity,  have  inflicted  every  kind  of  penalty,  from  the 
stake  to  the  stocks,  in  aid  of  your  reasoning ;  remember  that 
you,  Mother  Medicine,  have,  not  many  years  ago  applied  to 
Parliament  for  increase  of  forcible  hindrance  of  antipharma- 
copoeal  drenches,  pills,  and  powders.  Who  ever  heard  of  my 
asking  the  legislature  to  fine  blundering  circle-squarers  ?  Ee- 
member  that  the  D  in  dogma  is  the  D  in  decay ;  but  the  D  in 
demonstration  is  the  D  in  durability. 

I  have  known  a  medical  man — a  young  one — who  was  seriously 
of  opinion  that  the  country  ought  to  be  divided  into  medical 
parishes,  with  a  practitioner  appointed  to  each,  and  a  penalty 


MEDICAL  REFOKM.  159 

for  calling  in  any  but  the  incumbent  curer.  How  should  people 
know  how  to  choose  ?  The  hair-dressers  once  petitioned  Par- 
liament for  an  act  to  compel  people  to  wear  wigs.  My  own 
opinion  is  of  the  opposite  extreme,  as  in  the  following  letter 
(Examiner ',  April  5,  1856)  ;  which,  to  my  surprise,  I  saw  reprinted 
in  a  medical  journal,  as  a  plan  not  absolutely  to  be  rejected. 
I  am  perfectly  satisfied  that  it  would  greatly  promote  true 
medical  orthodoxy,  the  predominance  of  well  educated  thinkers, 
and  the  development  of  their  desirable  differences. 

SIR.  The  Medical  Bill  and  the  medical  question  generally  is 
one  on  which  experience  would  teach,  if  people  would  be  taught. 

The  great  soul  question  took  three  hundred  years  to  settle  :  the 
little  body  question  might  be  settled  in  thirty  years,  if  the  deci- 
sions in  the  former  question  were  studied. 

Time  was  when  the  State  believed,  as  honestly  as  ever  it 
believed  anything,  that  it  might,  could,  and  should  find  out 
true  doctrine  for  the  poor  ignorant  community ;  to  which,  like 
a  worthy  honest  state,  it  added  would.  Accordingly,  by  the 
assistance  of  a  Church,  which  undertook  the  physic,  the  surgery, 
and  the  pharmacy  of  sound  doctrine  all  by  itself,  it  sent  forth 
its  legally  qualified  teachers  into  every  parish,  and  woe  to  the 
man  who  called  in  any  other.  They  burnt  that  man,  they 
whipped  him,  they  imprisoned  him,  they  did  everything  but  what 
was  Christian  to  him,  all  for  his  soul's  health  and  the  amendment 
of  his  excesses. 

But  men  would  not  submit.  To  the  argument  that  the  State 
was  a  father  to  the  ignorant,  they  replied  that  it  was  at  best  the 
ignorant  father  of  an  ignorant  son,  and  that  a  blind  man  could 
find  his  way  into  a  ditch  without  another  blind  man  to  help  him. 
And  when  the  State  said — But  here  we  have  the  Church,  which 
knows  all  about  it,  the  ignorant  community  declared  that  it  had 
a  right  to  judge  that  question,  and  that  it  would  judge  it.  It 
also  said  that  the  Church  was  never  one  thing  long,  and  that  it 
progressed,  on  the  whole,  rather  more  slowly  than  the  ignorant 
community. 

The  end  of  it  was,  in  this  country,  that  every  one  who  chose 
taught  all  who  chose  to  let  him  teach,  on  condition  only  of  an  open 
and  true  registration.  The  State  was  allowed  to  patronise  one 
particular  Church,  so  that  no  one  need  trouble  himself  to  choose 
a  pastor  from  the  mere  necessity  of  choosing.  But  every  church 
is  allowed  its  colleges,  its  studies,  its  diplomas  ;  and  every  man 
is  allowed  his  choice.  There  is  no  proof  that  our  souls  are 


160  A  BUDGET  OF  PARADOXES. 

worse  off  than  in  the  sixteenth  century ;  and,  judging  by  fruits, 
there  is  much  reason  to  hope  they  are  better  off. 

Now  the  little  body  question  is  a  perfect  parallel  to  the  great 
soul  question  in  all  its  circumstances.  The  only  things  in  which 
the  parallel  fails  are  the  following :  Every  one  who  believes  in  a 
future  state  sees  that  the  soul  question  is  incomparably  more 
important  than  the  body  question,  and  every  one  can  try  the 
body  question  by  experiment  to  a  larger  extent  than  the  soul 
question.  The  proverb,  which  always  has  a  spark  of  truth  at  the 
bottom,  says  that  every  man  of  forty  is  either  a  fool  or  a 
physician  ;  but  did  even  the  proverb  maker  ever  dare  to  say  that 
every  man  is  at  any  age  either  a  fool  or  a  fit  teacher  of  religion  ? 

Common  sense  points  out  the  following  settlement  of  the 
medical  question :  and  to  this  it  will  come  sooner  or  later. 

Let  every  man  who  chooses — subject  to  one  common  law  of 
manslaughter  for  all  the  crass  cases — doctor  the  bodies  of  all 
who  choose  to  trust  him,  and  recover  payment  according  to 
agreement  in  the  courts  of  law.  Provided  always  that  every 
person  practising  should  be  registered  at  a  moderate  fee  in  a 
register  to  be  republished  every  six  months. 

Let  the  register  give  the  name,  address,  and  asserted  Qualifica- 
tion of  each  candidate — as  licentiate,  or  doctor,  or  what  not,  of 
this  or  that  college,  hall,  university,  &c.,  home  or  foreign.  Let 
it  be  competent  to  any  man  to  describe  himself  as  qualified  by 
study  in  public  schools  without  a  diploma,  or  by  private  study, 
or  even  by  intuition  or  divine  inspiration,  if  he  please.  But 
whatever  he  holds  his  qualification  to  be,  that  let  him  declare. 
Let  all  qualification  which  of  its  own  nature  admits  of  proof  be 
proved,  as  by  the  diploma  or  certificate,  &c.,  leaving  things  which 
cannot  be  proved,  as  asserted  private  study,  intuition,  inspiration, 
&c.,  to  work  their  own  way. 

Let  it  be  highly  penal  to  assert  to  the  patient  any  qualification 
which  is  not  in  the  register,  and  let  the  register  be  sold  very 
cheap.  Let  the  registrar  give  each  registered  practitioner  a  copy 
of  the  register  in  his  own  case ;  let  any  patient  have  power  to 
demand  a  sight  of  this  copy ;  and  let  no  money  for  attendance 
be  recoverable  in  any  case  in  which  there  has  been  false  repre- 
sentation. 

Let  any  party  in  any  suit  have  a  right  to  produce  what  medi- 
cal testimony  he  pleases.  Let  the  medical  witness  produce  his 
register,  and  let  his  evidence  be  for  the  jury,  as  is  that  of  an 
engineer  or  a  practitioner  of  any  art  which  is  not  attested  by 
diplomas. 


MEDICAL  REFORM—  REV.   R.   TAYLOR.  161 

Let  any  man  who  practises  without  venturing  to  put  his  name 
on  the  register  be  liable  to  fine  and  imprisonment. 

The  consequence  would  be  that,  as  now,  anybody  who  pleases 
might  practise  ;  for  the  medical  world  is  well  aware  that  there 
is  no  power  of  preventing  what  they  call  quacks  from  practising. 
But  very  different  from  what  is  now,  every  man  who  practises 
would  be  obliged  to  tell  the  whole  world  what  his  claim  is,  and 
would  run  a  great  risk  if  he  dared  to  tell  his  patient  in  private 
anything  different  from  what  he  had  told  the  whole  world. 

The  consequence  would  be  that  a  real  education  in  anatomy, 
physiology,  chemistry,  surgery,  and  what  is  known  of  the  thing 
called  medicine,  would  acquire  more  importance  than  it  now 
has. 

It  is  curious  to  see  how  completely  the  medical  man  of  the 
nineteenth  century  squares  with  the  priest  of  the  sixteenth  cen- 
tury. The  clergy  of  all  sects  are  now  better  divines  and  better 
men  than  they  ever  were.  They  have  lost  Bacon's  reproach  that 
they  took  a  smaller  measure  of  things  than  any  other  educated 
men  ;  and  the  physicians  are  now  in  this  particular  the  rear- 
guard of  the  learned  world  ;  though  it  may  be  true  that  the  rear 
in  our  day  is  further  on  in  the  march  than  the  van  of  Bacon's 
day.  Nor  will  they  ever  recover  the  lost  position  until  medicine 
is  as  free  as  religion. 

To  this  it  must  come.  To  this  the  public,  which  will  decide 
for  itself,  has  determined  it  shall  come.  To  this  the  public  has, 
in  fact,  brought  it,  but  on  a  plan  which  it  is  not  desirable  to 
make  permanent.  We  will  be  as  free  to  take  care  of  our  bodies 
as  of  our  souls  and  of  our  goods.  This  is  the  profession  of  all 
who  sign  as  I  do,  and  the  practice  of  most  of  those  who  would  not 
like  the  name  HETEROPATH.' 


The  motion  of  the  Sun  in  the  Ecliptic,  proved  to  be  uniform  in  a 
circular  orbit  .  .  .  with  preliminary  observations  on  the  fallacy 
of  the  Solar  System.  By  Bartholomew  Prescott,  1825,  8vo. 

The  author  had  published,  in  1803,  a  'Defence  of  the  Divine 
System,'  which  I  never  saw  ;  also,  '  On  the  inverted  scheme  of 
Copernicus.'  The  above  work  is  clever  in  its  satire. 

Manifesto  of  the  Christian  Evidence  Society,  established  Nov.  12, 
1824.  Twenty-four  plain  questions  to  honest  men. 

These  are  two  broadsides  of  August  and  November,  1826, 
signed  by  Robert  Taylor,  A.B.,  Orator  of  the  Christian  Evidence 


162  A  BUDGET  OF  PARADOXES. 

Society.  This  gentleman  was  a  clergyman,  and  was  convicted  of 
blasphemy  in  1827,  for  which  he  suffered  imprisonment,  and  got 
the  name  of  the  Devil's  Chaplain.  The  following  are  quota- 
tions :  — 

'  For  the  book  of  Revelation,  there  was  no  original  Greek  at  all,  but 
Erasmus  wrote  it  himself  in  Switzerland,  in  the  year  1516.  Bishop 
Marsh,  vol.  i.  p.  320.'- — '  Is  not  God  the  author  of  your  reason  ?  Can  he 
then  be  the  author  of  anything  which  is  contrary  to  your  reason  ?  If 
reason  be  a  sufficient  guide,  why  should  God  give  you  any  other  ?  if  it 
be  not  a  sufficient  guide,  why  has  he  given  you  that  ?  ' 

I  remember  a  votary  of  the  Society  being  asked  to  substitute  for 
reason  '  the  right  leg,'  and  for  guide  '  support,'  and  to  answer  the 
two  last  questions  :  he  said  there  must  be  a  quibble,  but  he  did 
not  see  what.  It  is  pleasant  to  reflect  that  the  argumentum  a, 
carcere  is  obsolete.  One  great  defect  of  it  was  that  it  did  not  go 
far  enough :  there  should  have  been  laws  against  subscriptions 
for  blasphemers,  against  dealing  at  their  shops,  and  against  rich 
widows  marrying  them. 

Had  I  taken  in  theology,  I  must  have  entered  books  against 
Christianity.  I  mention  the  above,  and  Paine's  '  Age  of  Reason,' 
simply  because  they  are  the  only  English  modern  works  that 
ever  came  in  my  way  without  my  asking  for  them.  The  three 
parts  of  the  '  Age  of  Reason '  were  published  in  Paris  1793,  Paris 
1795,  and  New  York  1807.  Carlile's  edition  is  of  London, 
1818,  8vo.  It  must  be  republished  when  the  time  comes,  to  show 
what  stuff  governments  and  clergy  were  afraid  of  at  the  begin- 
ning of  this  century.  I  should  never  have  seen  the  book,  if  it 
had  not  been  prohibited :  a  bookseller  put  it  under  my  nose  with 
a  fearful  look  round  him ;  and  I  could  do  no  less,  in  common 
curiosity,  than  buy  a  work  which  had  been  so  complimented  by 
church  and  state.  And  when  I  had  read  it,  I  said  in  my  mind  to 
church  and  state, — Confound  you  1  you  have  taken  me  in  worse 
than  any  reviewer  I  ever  met  with.  I  forget  what  I  gave  for 
the  book,  but  I  ought  to  have  been  able  to  claim  compensation 
somewhere. 


Cabbala  Algebraica.     Auctore  Gul.  Lud.  Christmann.  Stuttgard, 
1827,  4to. 

Eighty  closely  printed  pages  of  an  attempt  to  solve  equations 
of  every  degree,  which  has  a  process  called  by  the  author  cabbala. 
An  anonymous  correspondent  spells  cabbala  as  follows,  xaft/3a\\, 
and  makes  666  out  of  its  letters.  This  gentleman  has  sent  me, 


CABBALA   ALPHABETICA.  163 

since  my  Budget  commenced,  a  little  heap  of  satirical  communi- 
cations, each  having  a  666  or  two ;  for  instance,  alluding  to  my 
remarks  on  the  spelling  of  chemistry,  he  finds  the  fated  number  in 
^i/jLsia.  With  these  are  challenges  to  explain  them,  and  hints  about 
the  end  of  the  world.  All  these  letters  have  different  fantastic 
seals ;  one  of  them  with  the  legend  '  keep  your  temper,' — another 
bearing  *  bank  token  five  pence.'  The  only  signature  is  a  triangle 
with  a  little  circle  in  it,  which  I  interpret  to  mean  that  the 
writer  confesses  himself  to  be  the  round  man  stuck  in  the  three- 
cornered  hole,  to  be  explained  as  in  Sydney  Smith's  joke. 

There  is  a  kind  of  Cabbala  Alphabetica  which  the  investigators 
of  the  numerals  in  words  would  do  well  to  take  up :  it  is  the 
formation  of  sentences  which  contain  all  the  letters  of  the  alphabet, 
and  each  only  once.  No  one  has  done  it  with  v  and  j  treated  as 
consonants  ;  but  you  and  I  can  do  it.  Dr.  "Whewell  and  I  amused 
ourselves,  some  years  ago,  with  attempts.  He  could  not  make 
sense,  though  he  joined  words :  he  gave  me 

Phiz,  styx,  wrong,  buck,  flame,  quid. 

I  gave  him  the  following,  which  he  agreed  was  '  admirable 
sense  : '  I  certainly  think  the  words  would  never  have  come 
together  except  in  this  way : — 

I,  quartz  pyx,  who  fling  muck  beds. 

I  long  thought  that  no  human  being  could  say  this  under  any 
circumstances.  At  last  I  happened  to  be  reading  a  religious 
writer — as  he  thought  himself — who  threw  aspersions  on  his 
opponents  thick  and  threefold.  Heyday !  came  into  my  head, 
this  fellow  flings  muck  beds  ;  he  must  be  a  quartz  pyx.  And  then 
I  remembered  that  a  pyx  is  a  sacred  vessel,  and  quartz  is  a  hard 
stone,  as  hard  as  the  heart  of  a  religious  foe-curser.  So  that  the 
line  is  the  motto  of  the  ferocious  sectarian,  who  turns  his  religious 
vessels  into  mud-holders,  for  the  benefit  of  those  who  will  not 
see  what  he  sees. 

I    can    find    no    circumstances    for   the   following,   which    I 
received  from  another : — 

Fritz  !  quick  !  land  !  hew  gypsum  box. 
From  other  quarters  I  have  the  following  : — 
Dumpy  quiz  !  whirl  back  fogs  next. 

This  might  be  said  in  time  of  haze  to  the  queer  little  figure  in 


164  A  BUDGET   OF  PAKADOXES. 

the  Dutch  weather-toy,  which  comes  out  or  goes  in  with  the 
change  in  the  atmosphere.  Again, 

Export  my  fund !    Quiz  black  whigs. 

This  Squire  Western  might  have  said,  who  was  always  afraid  of 
the  whigs  sending  the  sinking-fund  over  to  Hanover.  But  the 
following  is  the  best :  it  is  good  advice  to  a  young  man,  very  well 
expressed  under  the  circumstances : — 

Get  nymph  ;  quiz  sad  brow  ;  fix  luck. 

"Which  in  more  sober  English  would  be,  Marry ;  be  cheerful ; 
watch  your  business.  There  is  more  edification,  more  religion  in 
this  than  in  all  the  666-interpretations  put  together. 

Such  things  would  make  excellent  writing  copies,  for  they 
secure  attention  to  every  letter ;  v  and  j  might  be  placed  at  the 
end. 

The  Celtic  Druids.    By  Godfrey  Higgins,  Esq.  of  Skellow  Grange, 

near  Doncaster.     London,  1827,  4to. 
Anacalypsis,  or  an  attempt  to  draw  aside  the  veil  of  the  Saitic 

Isis :  or  an  inquiry  into  the  origin  of  languages,  nations,  and 

religions.      By  Godfrey  Higgins,  &c London,  1836, 

2  vols.  4to. 

The  first  work  had  an  additional  preface  and  a  new  index  in 
1829.  Possibly,  in  future  time,  will  be  found  bound  up  with 
copies  of  the  second  work  two  sheets  which  Mr.  Higgins  circu- 
lated among  his  friends  in  1831 :  the  first  a  '  Eecapitulation,' the 
second  '  Book  vi.  ch.  1.' 

The  system  of  these  works  is  that — 

The  Buddhists  of  Upper  India  (of  whom  the  Phenician  Canaanite, 
Melchizedek,  was  a  priest),  who  built  the  Pyramids,  Stonehenge 
Carnac,  &c.  will  be  shown  to  have  founded  all  the  ancient  mythologies 
of  the  world,  which,  however  varied  and  corrupted  in  recent  times, 
were  originally  one,  and  that  one  founded  on  principles  sublime, 
beautiful,  and  true. 

These  works  contain  an  immense  quantity  of  learning,  very 
honestly  put  together.  I  presume  the  enormous  number  of  facts, 
and  the  goodness  of  the  index,  to  be  the  reasons  why  the  Ana- 
calypsis found  a  permanent  place  in  the  old  reading-room  of  the 
British  Museum,  even  before  the  change  which  greatly  increased 
the  number  of  books  left  free  to  the  reader  in  that  room. 

Mr.  Higgins,  whom  I  knew  well  in  the  last  six  years  of  his  life, 
and  respected  as  a  good,  learned,  and  (in  his  own  way) pious  man, 


GODFREY   HIGOINS.  165 

was  thoroughly  and  completely  the  man  of  a  system.  He  had 
that  sort  of  mental  connection  with  his  theory  that  made  his 
statements  of  his  authorities  trustworthy :  for,  besides  perfect 
integrity,  he  had  no  bias  towards  alteration  of  facts  :  he  saw  his 
system  in  the  way  the  fact  was  presented  to  him  by  his  authority, 
be  that  what  it  might. 

He  was  very  sure  of  a  fact  which  he  got  from  any  of  his 
authorities  :  nothing  could  shake  him.  Imagine  a  conversation 
between  him  and  an  Indian  officer  who  had  paid  long  attention 
to  Hindoo  antiquities  and  their  remains :  a  third  person  was 
present,  ego  qui  scribo.  G.  H.  'You  know  that  in  the  temples 
of  I-forget-who  the  Ceres  is  always  sculptured  precisely  as  in 

Greece.'  Col. ,  '  I  really  do  not  remember  it,  and  I  have 

seen  most  of  these  temples.'  G.  H.  '  It  is  so,  I  assure  you, 

especially  at  I-forget-where.'  Col. , 'Well,  I  am  sure!  I 

was  encamped  for  six  weeks  at  the  gate  of  that  very  temple,  and, 
except  a  little  shooting,  had  nothing  to  do  but  to  examine  its 
details,  which  I  did,  day  after  day,  and  I  found  nothing  of  the 
kind.'  It  was  of  no  use  at  all. 

Godfrey  Higgins  began  life  by  exposing  and  conquering,  at 
the  expense  of  two  years  of  his  studies,  some  shocking  abuses 
which  existed  in  the  York  Lunatic  Asylum.  This  was  a  pro- 
ceeding which  called  much  attention  to  the  treatment  of  the 
insane,  and  produced  much  good  effect.  He  was  very  resolute 
and  energetic.  The  magistracy  of  his  time  had  scruples  about 
using  the  severity  of  law  to  people  of  such  station  as  well-to-do 
farmers,  &c. :  they  would  allow  a  great  deal  of  resistance,  and 
endeavour  to  mollify  the  rebels  into  obedience.  A  young  farmer 
flatly  refused  to  pay  under  an  order  of  affiliation  made  upon  him 
by  Godfrey  Higgins.  He  was  duly  warned ;  and  persisted :  he 
shortly  found  himself  in  gaol.  He  went  there  sure  to  conquer 
the  Justice,  and  the  first  thing  he  did  was  to  demand  to  see  his 
lawyer.  He  was  told,  to  his  horror,  that  as  soon  as  he  had  been 
cropped  and  prison-dressed,  he  might  see  as  many  lawyers  as  he 
pleased,  to  be  looked  at,  laughed  at,  and  advised  that  there  was 
but  one  way  out  of  the  scrape.  Higgins  was,  in  his  speculations, 
a  regular  counterpart  of  Bailly  ;  but  the  celebrated  Mayor  of  Paris 
had  not  his  nerve.  It  is  impossible  to  say,  if  their  characters  had 
been  changed,  whether  the  unfortunate  crisis  in  which  Bailly  was 
not  equal  to  the  occasion  would  have  led  to  very  different  results 
if  Higgins  had  been  in  his  place :  but  assuredly  constitutional 
liberty  would  have  had  one  chance  more.  There  are  two  works 
of  his  by  which  he  was  known,  apart  from  his  paradoxes. 


166  A   BUDGET   OF   PARADOXES. 

First,  '  An  apology  for  the  life  and  character  of  the  celebrated 
prophet  of  Arabia,  called  Mohamed,  or  the  Illustrious.'  London, 
8vo.  1829.  The  reader  will  look  at  this  writing  of  our  English 
Buddhist  with  suspicious  eye,  but  he  will  not  be  able  to  avoid 
confessing  that  the  Arabian  prophet  has  some  reparation  to 
demand  at  the  hands  of  Christians.  Next,  '  Horse  Sabbaticse ;  or 
an  attempt  to  correct  certain  superstitions  and  vulgar  errors 
respecting  the  Sabbath.  Second  edition,  with  a  large  appendix.' 
London,  12mo.  1833.  This  book  was  very  heterodox  at  the 
time,  but  it  has  furnished  material  for  some  of  the  clergy  of  our 
day. 

I  never  could  quite  make  out  whether  Godfrey  Higgins  took 
that  system  which  he  traced  to  the  Buddhists  to  have  a  Divine 
origin,  or  to  be  the  result  of  good  men's  meditations.  Himself  a 
strong  theist,  and  believer  in  a  future  state,  one  would  suppose 
that  he  would  refer  a  universal  religion,  spread  in  different  forms 
over  the  whole  earth  from  one  source,  directly  to  the  universal 
Parent.  And  this  I  suspect  he  did,  whether  he  knew  it  or  not. 
The  external  evidence  is  balanced.  In  his  preface  he  says — 

*  I  cannot  help  smiling  when  I  consider  that  the  priests  Lave  objected 
to  admit  my  former  book,  "  the  Celtic  Druids,"  into  libraries,  because 
it  was  antichristian ;  and  it  has  been  attacked  by  Deists,  because  it 
•was  superfluously  religious.  The  learned  Deist,  the  Rev.  R.  Taylor 
[already  mentioned],  has  designated  me  as  tlie  religious  Mr.  Higgins.' 

The  time  will  come  when  some  profound  historian  of  literature 
will  make  himself  much  clearer  on  the  point  than  I  am. 

The  triumphal  Chariot  of  Friction  :  or  a  familiar  elucidation  of 
the  origin  of  magnetic  attraction,  &c.  &c.  By  William  Pope. 
London,  1829,  4to. 

Part  of  this  work  is  on  a  dipping-needle  of  the  author's  con- 
struction. It  must  have  been  under  the  impression  that  a  book 
of.  naval  magnetism  was  proposed,  that  a  great  many  officers,  the 
Royal  Naval  Club,  &c.  lent  their  names  to  the  subscription  list. 
How  must  they  have  been  surprised  to  find,  right  opposite  to  the 
list  of  subscribers,  the  plate  presenting  '  the  three  emphatic  letters, 
J.  A.  0.'  And  how  much  more  when  they  saw  it  set  forth  that  if 
a  square  be  inscribed  in  a  circle,  a  circle  within  that,  then  a 
square  again,  &c.,  it  is  impossible  to  have  more  than  fourteen 
circles,  let  the  first  circle  be  as  large  as  you  please.  From  this 
the  seven  attributes  of  Grod  are  unfolded ;  and  further,  that  all 
matter  was  moral,  until  Lucifer  churned  it  into  physical  '  as  far 


JACOTOT — TRACT  ON  PROBABILITY.  .    167 

as  the  third  circle  in  Deity ' :  this  Lucifer,  called  Leviathan  in 
Job,  being  thus  the  moving  cause  of  chaos.  I  shall  say  no  more, 
except  that  the  friction  of  the  air  is  the  cause  of  magnetism. 

Remarks  on  the  Architecture,  Sculpture,  and  Zodiac  of  Palmyra ; 
with  a  Key  to  the  Inscriptions.  By  B.  Prescot.  London, 
1830,  8vo. 

Mr.  Prescot  gives  the  signs  of  the  zodiac  a  Hebrew  origin. 

Epitome  de  matheinatiques.  Par  F.  Jacotot,  Avocat.  3ieme  edition. 

Paris,  1830,  8vo.  (pp.  18). 
Methode  Jacotot.      Choix  de  propositions  mathematiques.     Par 

P.  Y.  de  Sepres.     2nde  edition.     Paris,  1830,  8vo.  (pp.  82). 

Of  Jacotot's  method,  which  had  some  vogue  in  Paris,  the 
principle  was  Tout  est  dans  tout,  and  the  process  Apprendre 
quelque  chose,  et  a  y  rapporter  tout  le  reste.  The  first  tract  has 
a  proposition  in  conic  sections  and  its  preliminaries :  the  second 
has  twenty  exercises,  of  which  the  first  is  finding  the  greatest 
common  measure  of  two  numbers,  and  the  last  is  the  motion  of  a 
point  on  a  surface,  acted  on  by  given  forces.  This  is  topped  up 
with  the  problem  of  sound  in  a  tube,  and  a  slice  of  Laplac^s 
theory  of  the  tides.  All  to  be  studied  until  known  by  heart,  and 
all  the  rest  will  come,  or  at  least  join  on  easily  when  it  conies. 
There  is  much  truth  in  the  assertion  that  new  knowledge  hooks 
on  easily  to  a  little  of  the  old,  thoroughly  mastered.  The  day  is 
coming  when  it  will  be  found  out  that  crammed  erudition,  got  up 
for  examinations,  does  not  cast  out  any  hooks  for  more. 

Lettre  a  MM.  les  Membres  de  1'Academie  Boyale  des  Sciences, 
contenant  un  developpement  de  la  refutation  du  systeme  de  la 
gravitation  universelle,  qui  leur  a  etc  presentee  le  30  aout,  1830. 
Par  Felix  Passot.  Paris,  1830,  8vo. 

Works  of  this  sort  are  less  common  in  France  than  in  England. 
In  France  there  is  only  the  Academy  of  Sciences  to  go  to  :  in 
England  there  is  a  reading  public  out  of  the  Eoyal  Society,  &c. 

About  1830  was  published,  in  the  Librai^y  of  Useful  Know- 
ledge, the  tract  on  Probability,  the  joint  work  of  the  late  Sir 
John  Lubbock  and  Mr.  Driukwater  (Bethune).  It  is  one  of  the 
best  elementary  openings  of  the  subject.  A  binder  put  my  name 
on  the  outside  (the  work  was  anonymous)  and  the  consequence 
was  that  nothing  could  drive  out  of  people's  heads  that  it  was 


168  A  BUDGET   OF  PAKADOXES. 

written  by  me.  I  do  not  know  how  many  denials  I  have  made, 
from  a  passage  in  one  of  my  own  works  to  a  letter  in  the  Times : 
and  I  am  not  sure  that  I  have  succeeded  in  establishing  the 
truth,  even  now.  I  accordingly  note  the  fact  once  more.  But 
as  a  book  has  no  right  here  unless  it  contain  a  paradox — or  thing 
counter  to  general  opinion  or  practice — I  will  produce  two  small 
ones.  Sir  John  Lubbock,  with  whom  lay  the  executive  arrange- 
ment, had  a  strong  objection  to  the  last  word  in  '  Theory  of 
Probabilities,'  he  maintained  that  the  singular  probability,  should 
be  used  ;  and  I  hold  him  quite  right. 

The  second  case  was  this :  My  friend  Sir  J.  L.,  with  a  large 
cluster  of  intellectual  qualities,  and  another  of  social  qualities, 
had  one  point  of  character  which  I  will  not  call  bad  and  cannot 
call  good  ;  he  never  used  a  slang  expression.  To  such  a  length 
did  he  carry  his  dislike,  that  he  could  not  bear  head  and  tail, 
even  in  a  work  on  games  of  chance  :  so  he  used  obverse  and  reverse. 
I  stared  when  I  first  saw  this  :  but,  to  my  delight,  I  found  that 
the  force  of  circumstances  beat  him  at  last.  He  was  obliged  to 
take  an  example  from  the  race-course,  and  the  name  of  one  of 
the  horses  was  Bessy  Bedlam !  And  he  did  not  put  her  down  as 
Elizabeth  Bethlehem,  but  forced  himself  to  follow  the  jockeys. 
• 

[Almanach  Remain  sur  la  Loterie  Royale  de  France,  ou  les 
Utrennes  necessaires  aux  Actionnaires  et  Receveurs  de  la  dite 
Loterie.  Par  M.  Menut  de  St.-Mesmin.  Paris,  1830.  12mo. 

This  book  contains  all  the  drawings  of  the  French  lottery  (two 
or  three,  each  month)  from  1758  to  1830.  It  is  intended  for 
those  who  thought  they  could  predict  the  future  drawings  from 
the  past :  and  various  sets  of  sympathetic  numbers  are  given  to 
help  them.  The  principle  is,  that  anything  which  has  not 
happened  for  a  long  time  must  be  soon  to  come.  At  rouge  et 
noir,  for  example,  when  the  red  has  won  five  times  running, 
sagacious  gamblers  stake  on  the  black,  for  they  think  the  turn 
which  must  come  at  last  is  nearer  than  it  was.  So  it  is  :  but 
observation  would  have  shown  that  if  a  large  number  of  those 
cases  had  been  registered  which  show  a  run  of  five  for  the  red, 
the  next  game  would  just  as  often  have  made  the  run  into  six 
as  have  turned  in  favour  of  the  black.  But  the  gambling 
reasoner  is  incorrigible :  if  he  would  but  take  to  squaring  the 
circle,  what  a  load  of  misery  would  be  saved.  A  writer  of  1823, 
who  appeared  to  be  thoroughly  acquainted  with  the  gambling  of 
Paris  and  London,  says  that  the  gamesters  by  profession  are 
haunted  by  a  secret  foreboding  of  their  future  destruction,  and 


PAKADOXES  OF  CHANCE.  169 

seem  as  if  they  said  to  the  banker  at  the  table,  as  the  gladiators 
said  to  the  emperor,  Morituri  te  salutant. 

In  the  French  lottery,  five  numbers  out  of  ninety  were  drawn 
at  a  time.  Any  person,  in  any  part  of  the  country,  might  stake 
any  sum  upon  any  event  he  pleased,  as  that  27  should  be  drawn  ; 
that  42  and  81  should  be  drawn ;  that  42  and  81  should  be 
drawn,  and  42  first ;  and  so  on  up  to  a  quine  determine,  if  he 
chose,  which  is  betting  on  five  given  numbers  in  a  given  order. 
Thus,  in  July,  1821,  one  of  the  drawings  was 

8        46        16        64        13. 

A  gambler  had  actually  predicted  the  five  numbers  (but  not 
their  order),  and  won  131,350  francs  on  a  trifling  stake.  M. 
Menut  seems  to  insinuate  that  the  hint  what  numbers  to  cnoose 
was  given  at  his  own  office.  Another  won  20,852  francs  on  the 
quaterne  8,  16,  46,  64,. in  this  very  drawing.  These  gains,  of 
course,  were  widely  advertised :  of  the  multitudes  who  lost 
nothing  was  said.  The  enormous  number  of  those  who  played 
is  proved  to  all  who  have  studied  chances  arithmetically  by  the 
numbers  of  simple  quaternes  which  were  gained  :  in  1 822,  four- 
teen;  in  1823,  six  ;  in  1824,  sixteen;  in  1825,  nine,  &c. 

The  paradoxes  of  what  is  called  chance,  or  hazard,  might  them- 
selves make  a  small  volume.  All  the  world  understands  that 
there  is  a  long  run,  a  general  average ;  but  great  part  of  the 
world  is  surprised  that  this  general  average  should  be  computed 
and  predicted.  There  are  many  remarkable  cases  of  verification ; 
and  one  of  them  relates  to  the  quadrature  of  the  circle.  I  give 
some  account  of  this  and  another.  Throw  a  penny  time  after 
time  until  head  arrives,  which  it  will  do  before  long :  let  this 
be  called  a  set.  Accordingly,  H  is  the  smallest  set,  TH  the  next 
smallest,  then  TTH,  &c.  For  abbreviation,  let  a  set  in  which 
seven  tails  occur  before  head  turns  up  be  T7H.  In  an  immense 
number  of  trials  of  sets,  about  half  will  be  H ;  about  a  quarter 
TH;  about  an  eighth,  T2H.  Buffon  tried  2,048  sets;  and 
several  have  followed  him.  It  will  tend  to  illustrate  the  prin- 
ciple if  I  give  all  the  results ;  namely,  that  many  trials  will 
with  moral  certainty  show  an  approach — and  the  greater  the 
greater  the  number  of  trials — to  that  average  which  sober  reason- 
ing predicts.  In  the  first  column  is  the  most  likely  number  of 
the  theory :  the  next  column  gives  BufTon's  result ;  the  three 
next  are  results  obtained  from  trial  by  correspondents  of  mine. 
In  each  case  the  number  of  trials  is  2,048. 


170  A    BUDGET  OF  PAEADOXES. 


H 

1,024    . 

1,061     . 

1,048     .    1,017     . 

1,039 

TH      . 

512     . 

494     . 

507     . 

547    . 

480 

T2H    . 

256     . 

232     . 

248     . 

235     . 

267 

T'H    . 

128    . 

137    . 

99'   , 

118    . 

126 

T<H    . 

64    . 

56     . 

71    . 

72    -. 

67 

T5H    . 

32    . 

29     . 

38    . 

32    . 

33 

T6H    . 

16     . 

.    25     . 

17    . 

30    . 

19 

T7H    , 

8     . 

8    . 

9     . 

9    . 

10 

T8H    . 

4    . 

6    . 

,      5     . 

3     . 

3 

T9H    . 

2     . 

3    . 

2     . 

4 

Tl°H   . 

1     . 

1     . 

1 

TnH 

0     . 

1 

T12H 

0    . 

0 

T13H 

1     . 

1     . 

0 

TuH 

0    . 

0 

T15H 

1   . 

1 

&c. 

0 

0 

2,048     .    2,048     .    2,048     .    2,048     .    2,048 

In  very  many  trials,  then,  we  may  depend  upon  something  like 
the  predicted  average.  Conversely,  from  many  trials  we  may 
form  a  guess  at  what  the  average  will  be.  Thus,  in  Buffon's 
experiment  the  2,048  first  throws  of  the  sets  gave  head  in  1,061 
cases :  we  have  a  right  to  infer  that  in  the  long  run  something 
like  1,061  out  of  2,048  is  the  proportion  of  heads,  even  before 
we  know  the  reasons  for  the  equality  of  chance,  which  tell  us  that 
1,024  out  of  2,048  is  the  real  truth.  I  now  come  to  the  way  in 
which  such  considerations  have  led  to  a  mode  in  which  mere 
pitch-and-toss  has  given  a  more  accurate  approach  to  the  quadra- 
ture of  the  circle  than  has  been  reached  by  some  of  my  para- 
doxers.  What  would  my  friend1  in  No.  14  have  said  to  this? 
The  method  is  as  follows :  Suppose  a  planked  floor  of  the  usual 
kind,  with  thin  visible  seams  between  the  planks.  Let  there  be 
a  thin  straight  rod,  or  wire,  not  so  long  as  the  breadth  of  the 
plank.  This  rod,  being  tossed  up  at  hazard,  will  either  fall  quite 
clear  of  the  seams,  or  will  lay  across  one  seam.  Now  BufFon, 
and  after  him  Laplace,  proved  the  following :  That  in  the  long 
run  the  fraction  of  the  whole  number  of  trials  in  which  a  seam 
is  intersected  will  be  the  fraction  which  twice  the  length  of  the 
rod  is  of  the  circumference  of  the  circle  having  the  breadth  of  a 
plank  for  its  diameter.  In  1855  Mr.  Ambrose  Smith,  of  Aber- 
deen, made  3,204  trials  with  a  rod  three-fifths  of  the  distance 
between  the  planks:  there  were  1,213  clear  intersections,  and 
1 1  contacts  on  which  it  was  difficult  to  decide.  Divide  these 

1  See  p.  172.     This  article  was  a  supplement  to  No.  14  in  the  Athen&um  Budget. 


THE  INTERMINABLE   FRACTION   TT.  171 

contacts  equally,  and  we  have  1,218^  to  3,204  for  the  ratio  of  6 
to  5?r,  presuming  that  the  greatness  of  the  number  of  trials  gives 
something  near  to  the  final  average,  or  result  in  the  long  run  : 
this  gives  7r=3'1553.  If  all  the  11  contacts  had  been  treated  as 
intersections,  the  result  would  have  been  77  =  3'  141  2,  exceedingly 
near.  A  pupil  of  mine  made  600  trials  with  a  rod  of  the  length 
between  the  seams,  and  got  ?r=3'137. 

This  method  will  hardly  be  believed  until  it  has  been  re- 
peated so  often  that  '  there  never  could  have  been  any  doubt 
about  it.' 

The  first  experiment  strongly  illustrates  a  truth  of  the  theory, 
well  confirmed  by  practice  :  whatever  can  happen  will  happen  if  we 
make  trials  enough.  Who  would  undertake  to  throw  tail  eight 
times  running?  Nevertheless,  in  the  8,192  sets  tail  8  times 
running  occurred  17  times  ;  9  times  running,  9  times  ;  10  times 
running,  twice;  11  times  and  13  times,  each  once;  and  15  times, 
twice.] 

1830.  The  celebrated  interminable  fraction  3-14159.  .  .  ,  which 
the  mathematician  calls  TT,  is  the  ratio  of  the  circumference  to 
the  diameter.  But  it  is  thousands  of  things  besides.  It  is  con- 
stantly turning  up  in  mathematics  :  and  if  arithmetic  and  algebra 
had  been  studied  without  geometry,  IT  must  have  come  in  some- 
how, though  at  what  stage  or  under  what  name  must  have 
depended  upon  the  casualties  of  algebraical  invention.  This  will 
readily  be  seen  when  it  is  stated  that  TT  is  nothing  but  four  times 
the  series 


ad  infinitum.  It  would  be  wonderful  if  so  simple  a  series  had 
but  one  kind  of  occurrence.  As  it  is,  our  trigonometry  being 
founded  on  the  circle,  TT  first  appears  as  the  ratio  stated.  If,  for 
instance,  a  deep  study  of  probable  fluctuation  from  the  average 
had  preceded  geometry,  TT  might  have  emerged  as  a  number 
perfectly  indispensable  in  such  problems  as  —  What  is  the  chance 
of  the  number  of  aces  lying  between  a  million  +  x  and  a  million 
—  x,  when  six  million  of  throws  are  made  with  a  die  ?  I  have  not 
gone  into  any  detail  of  all  those  cases  in  which  the  paradoxer 
finds  out,  by  his  unassisted  acumen,  that  results  of  mathematical 
investigation  cannot  be  :  in  fact,  this  discovery  is  only  an  accom- 
paniment, though  a  necessary  one,  of  his  paradoxical  statement  of 
that  which  must  be.  Logicians  are  beginning  to  see  that  the 
notion  of  horse  is  inseparably  connected  with  that  of  non-horse  : 
that  the  first  without  the  second  would  be  no  notion  at  all.  And 
it  is  clear  that  the  positive  affirmation  of  that  -which  contradicts 


172  A   BUDGET   OF  PAEADOXES. 

mathematical  demonstration  cannot  but  be  accompanied  by  a 
declaration,  mostly  overtly  made,  that  demonstration  is  false.  If 
the  mathematician  were  interested  in  punishing  this  indiscretion, 
he  could  make  his  denier  ridiculous  by  inventing  asserted  results 
which  would  completely  take  him  in. 

More  than  thirty  years  ago  I  had  a  friend,  now  long  gone,  who 
was  a  mathematician,  but  not  of  the  higher  branches :  he  was, 
inter  alia,  thoroughly  up  in  all  that  relates  to  mortality,  life 
assurance,  &c.  One  day,  explaining  to  him  how  it  should  be 
ascertained  what  the  chance  is  of  the  survivors  of  a  large  number 
of  persons  now  alive  lying  between  given  limits  of  number  at  the 
end  of  a  certain  time,  I  came,  of  course,  upon  the  introduction  of 
TT,  which  I  could  only  describe  as  the  ratio  of  the  circumference 
of  a  circle  to  its  diameter.  '  Oh,  my  dear  friend  !  that  must  be 
a  delusion ;  what  can  the  circle  have  to  do  with  the  numbers 
alive  at  the  end  of  a  given  time  ? ' — '  I  cannot  demonstrate  it  to 
you;  but  it  is  demonstrated.' — 'Oh!  stuff!  I  think  you  can 
prove  anything  with  your  differential  calculus  :  figment,  depend 
upon  it.'  I  said  no  more  ;  but,  a  few  days  afterwards,  I  went  to 
him  and  very  gravely  told  him  that  I  had  discovered  the  law  of 
human  mortality  in  the  Carlisle  Table,  of  which  he  thought  very 
highly.  I  told  him  that  the  law  was  involved  in  this  circum- 
stance. Take  the  table  of  expectation  of  life,  choose  any  age, 
take  its  expectation  and  make  the  nearest  integer  a  new  age,  do 
the  same  with  that,  and  so  on ;  begin  at  what  age  you  like,  you 
are  sure  to  end  at  the  place  where  the  age  past  is  equal,  or  most 
nearly  equal,  to  the  expectation  to  come.  '  You  don't  mean  that 
this  always  happens  ?  ' — '  Try  it.'  He  did  try,  again  and  again ; 
and  found  it  as  I  said.  '  This  is,  indeed,  a  curious  thing ;  this  is 
a  discovery.'  I  might  have  sent  him  about  trumpeting  the  law 
of  life  :  but  I  contented  myself  with  informing  him  that  the  same 
thing  would  happen  with  any  table  whatsoever  in  which  the  first 
column  goes  up  and  the  second  goes  down  ;  and  that  if  a  pro- 
ficient in  the  higher  mathematics  chose  to  palm  a  figment  upon 
him,  he  could  do  without  the  circle  :  a  corsaire,  corsaire  et  demi, 
the  French  proverb  says.  'Oh  !'  it  was  remarked,  'I  see,  this  was 
Milne  ! '  It  was  not  Milne  :  I  remember  well  showing  the  formula 
to  him  some  time  afterwards.  He  raised  no  difficulty  about  TT  ; 
he  knew  the  forms  of  Laplace's  results,  and  he  was  much  "in- 
terested. Besides,  Milne  never  said  stuff !  and  figment !  And  he 
would  not  have  been  taken  in  :  he  would  have  quietly  tried  it 
with  the  Northampton  and  all  the  other  tables,  and  would  have 
grot  at  the  truth. 


EUCLID  WITHOUT   AXIOMS.  173 

The  first  book  of  Euclid's  Elements.  With  alterations  and 
familiar  notes.  Being  an  attempt  to  get  rid  of  axioms  alto- 
gether ;  and  to  establish  the  theory  of  parallel  lines,  without 
the  introduction  of  any  principle  not  common  to  other  parts  of 
the  elements.  By  a  member  of  the  University  of  Cambridge. 
Third  edition.  In  usum  serenissimje  filiolae.  London,  1830. 

The  author  was  Lieut. -Col.  (now  General)  Perronet  Thompson, 
the  author  of  the  '  Catechism  on  the  Corn  Laws.'  I  reviewed  the 
fourth  edition — which  had  the  name  of  '  Geometry  without 
Axioms,'  1833 — in  the  quarterly  Journal  of  Education  for 
January,  1834.  Col.  Thompson,  who  then  was  a  contributor  to — 
if  not  editor  of — the  Westminster  Review,  replied  in  an  article 
the  authorship  of  which  could  not  be  mistaken. 

Some  more  attempts  upon  the  problem,  by  the  same  author, 
will  be  found  in  the  sequel.  They  are  all  of  acute  and  legitimate 
speculation  ;  but  they  do  not  conquer  the  difficulty  in  the  manner 
demanded  by  the  conditions  of  the  problem.  The  paradox  of 
parallels  does  not  contribute  much  to  my  pages  :  its  cases  are  to 
be  found  for  the  most  part  in  geometrical  systems,  or  in  notes  to 
them.  Most  of  them  consist  in  the  proposal  of  additional  pos- 
tulates ;  some  are  attempts  to  do  without  any  new  postulate. 
Gen.  Perronet  Thompson,  whose  paradoxes  are  always  constructed 
on  much  study  of  previous  writers,  has  collected  in  the  work 
above-named,  a  budget  of  attempts,  the  heads  of  which  are  in  the 
Penny  and  English  Cyclopaedias,  at  '  Parallels.'  He  has  given 
thirty  instances,  selected  from  what  he  had  found. 

Lagrange,  in  one  of  the  later  years  of  his  life,  imagined  that  he 
had  overcome  the  difficulty.  He  went  so  far  as  to  write  a  paper, 
which  he  took  with  him  to  the  Institute,  and  began  to  read  it. 
But  in  the  first  paragraph  something  struck  him  which  he  had 
not  observed  :  he  muttered  II  faut  que  fy  songe  encore,  and  put 
the  paper  in  his  pocket. 


The  following  paragraph  appeared  in  the  Morning  Post, 
May  4,  1831  :— 

'  We  understand  that  although,  owing  to  circumstances  with  which 
the  public  are  uot  concerned,  Mr.  Groulburn  declined  becoming  a 
candidate  for  University  honours,  that  his  scientific  attainments  are 
far  from  inconsiderable.  He  is  well  known  to  be  the  author  of  an 
essay  in  the  Philosophical  Transactions  on  the  accurate  rectification  of 
a  circular  arc,  and  of  an  investigation  of  the  equation  of  a  lunar 


174  A  BUDGET   OF  PARADOXES. 

caustic — a  problem  likely  to   become  of  great  use   in  nautical   as- 
tronomy.' 

This  hoax — which  would  probably  have  succeeded  with  any 
journal — was  palmed  upon  the  Morning  Post.,  which  supported 
Mr.  Goulburn,  by  some  Cambridge  wags  who  supported  Mr. 
Lubbock,  the  other  candidate  for  the  University  of  Cambridge. 
Putting  on  the  usual  concealment,  I  may  say  that  I  always  sus- 
pected Dr-nkw-t-r  B-th-n-  of  having  a  share  in  the  matter.  The 
skill  of  the  hoax  lies  in  avoiding  the  words  '  quadrature  of  the 
circle,'  which  all  know,  and  speaking  of  '  the  accurate  rectification 
of  a  circular  arc,'  which  all  do  not  know  for  its  synonyme.  The 
Morning  Post  next  day  gave  a  reproof  to  hoaxers  in  general, 
without  referring  to  any  particular  case.  It  must  be  added, 
that  although  there  are  caustics  in  mathematics,  there  is  no 
lunar  caustic. 

So  far  as  Mr.  Groulburn  was  concerned,  the  above  was  poetic 
justice.  He  was  the  minister  who,  in  the  old  time,  told  a  depu- 
tation from  the  Astronomical  Society  that  the  Government  '  did 
not  care  twopence  for  all  the  science  in  the  country.'  There  may 
be  some  still  alive  who  remember  this  :  I  heard  it  from  more  than 
one  of  those  who  were  present,  and  are  now  gone.  Matters  are 
much  changed.  I  was  thirty  years  in  office  at  the  Astronomical 
Society ;  and,  to  my  certain  knowledge,  every  Government  of  that 
period,  Whig  and  Tory,  showed  itself  ready  to  help  with  influence 
when  wanted,  and  with  money  whenever  there  was  an  answer  for 
the  House  of  Commons.  The  following  correction  subsequently 
appeared.  Referring  to  the  hoax  about  Mr.  Groulburn,  Messrs.  C. 
H.  and  Thompson  Cooper  have  corrected  an  error,  by  stating  that 
the  election  which  gave  rise  to  the  hoax  was  that  in  which  Messrs. 
Groulburn  and  Yates  Peel  defeated  Lord  Palmerston  and  Mr. 
Cavendish.  They  add  that  Mr.  Gunning,  the  well-known  Esquire 
Bedell  of  the  University,  attributed  the  hoax  to  the  late  Eev.  R. 
Sheepshanks,  to  whom,  they  state,  are  also  attributed  certain  clever 
fictitious  biographies — of  public  men,  as  I  understand  it — which 
were  palmed  upon  the  editor  of  the  Cambridge  Chronicle,  who 
never  suspected  their  genuineness  to  the  day  of  his  death.  Being 
in  most  confidential  intercourse  with  Mr.  Sheepshaaks,  both  at  the 
time  and  all  the  rest  of  his  life  (twenty-five  years),  and  never 
having  heard  him  allude  to  any  such  things— which  were  not  in 
his  line,  though  he  had  satirical  power  of  quite  another  kind — I 
feel  satisfied  he  had  nothing  to  do  with  them.  I  may  add  that 
others,  his  nearest  friends,  and  also  members  of  his  family,  never 


SCIENTIFIC   ELECTION   SQUIB.  175 

heard  him  allude  to  these  hoaxes  as  their  author,  and  disbelieve 
his  authorship  as  much  as  I  do  myself.  I  say  this  not  as  imputing 
any  blame  to  the  true  author,  such  hoaxes  being  fair  election 
jokes  in  all  time,  but  merely  to  put  the  saddle  off  the  wrong  horse, 
and  to  give  one  more  instance  of  the  insecurity  of  imputed 
authorship.  Had  Mr.  Sheepshanks  ever  told  me  that  he  had 
perpetrated  the  hoax,  I  should  have  had  no  hesitation  in  giving 
it  to  him.  I  consider  all  clever  election  squibs,  free  from  bitter- 
ness and  personal  imputation,  as  giving  the  multitude  good 
channels  for  the  vent  of  feelings  which  but  for  them  would  cer- 
tainly find  bad  ones. 

[  But  I  now  suspect  that  Mr.  Babbage  had  some  hand  in  the 
hoax.  He  gives  it  in  his  '  Passages,  &c.'  and  is  evidently  writing 
from  memory,  for  he  gives  the  wrong  year.  But  he  has  given  the 
paragraph,  though  not  accurately,  yet  with  such  a  recollection  of 
the  points  as  brings  suspicion  of  the  authorship  upon  him,  perhaps 
in  conjunction  with  D.  B.  Both  were  on  Cavendish's  committee. 
Mr.  Babbage  adds,  that  '  late  one  evening  a  cab  drove  up  in  hot 
haste  to  the  office  of  the  Morning  Post,  delivered  the  copy  as 
coming  from  Mr.  Gmilburn's  committee,  and  at  the  same  time 
ordered  fifty  extra  copies  of  the  Post  to  be  sent  next  morning  to 
their  committee-room.  I  think  the  man — the  only  one  I  ever 
heard  of — who  knew  all  about  the  cab  and  the  extra  copies  must 
have  known  more.] 

Demonville. — A  Frenchman's  Christian  name  is  his  own  secret, 
unless  there  be  two  of  the  surname.  M.  Demonville  is  a  very 
good  instance  of  the  difference  between  a  French  and  English 
discoverer.  In  England  there  is  a  public  to  listen  to  discoveries 
in  mathematical  subjects  made  without  mathematics :  a  public 
which  will  hear,  and  wonder,  and  think  it  possible  that  the  pre- 
tensions of  the  discoverer  have  some  foundation.  The  unnoticed 
man  may  possibly  be  right :  and  the  old  country-town  reputation 
which  I  once  heard  of,  attaching  to  a  man  who  *  had  written  a 
book  about  the  signs  of  the  zodiac  which  all  the  philosophers  in 
London  could  not  answer,'  is  fame  as  far  as  it  goes.  Accordingly, 
we  have  plenty  of  discoverers  who,  even  in  astronomy,  pronounce 
the  learned  in  error  because  of  mathematics.  In  France,  beyond 
the  sphere  of  influence  of  the  Academy  of  Sciences,  there  is  no 
one  to  cast  a  thought  upon  the  matter :  all  who  take  the  least 
interest  repose  entire  faith  in  the  Institute.  Hence  the  French 
discoverer  turns  all  his  thoughts  to  the  Institute,  and  looks  for 


176  A  BUDGET   OF  PARADOXES. 

his  only  hearing  in  that  quarter.  He  therefore  throws  no  slur 
upon  the  means  of  knowledge,  but  would  say,  with  M.  Demon- 
ville — '  A  1'egard  de  M.  Poisson,  j'envie  loyalement  la  millieme 
partie  de  ses  connaissances  mathematiques,  pour  prouver  mon 
systeme  d'astronomie  aux  plus  incredules.'  This  system  is  that 
the  only  bodies  of  our  system  are  the  earth,  the  sun,  and  the 
moon ;  all  the  others  being  illusions,  caused  by  reflexion  of  the 
sun  and  moon  from  the  ice  of  the  polar  regions.  In  mathematics, 
addition  and  subtraction  are  for  men  ;  multiplication  and  division, 
which  are  in  truth  creation  and  destruction,  are  prerogatives  of 
Deity.  But  nothing  multiplied  by  nothing  is  one.  M.  Demon- 
ville  obtained  an  introduction  to  William  the  Fourth,  who  desired 
the  opinion  of  the  Eoyal  Society  upon  his  system :  the  answer 
was  very  brief.  The  King  was  quite  right ;  so  was  the  Society  : 
the  fault  lay  with  those  who  advised  His  Majesty  on  a  matter 
they  knew  nothing  about.  The  writings  of  M.  Demonville  in  my 
possession  are  as  follows.  The  dates — which  were  only  on  covers 
torn  off  in  binding — were  about  1831-34  : — 

'  Petit  cours  d'astronomie'  followed  by  '  Sur  1'unite  mathematique.' 
— Principes  de  la  physique  de  la  creation  implicitement  admis  dans  la 
notice  sur  le  tonnerre  par  M.  Arago. — Question  de  longitude  sur 
mer. — Vrai  systeme  du  monde  (pp.  92).  Same  title,  four  pages,  small 
type.  Same  title,  four  pages,  addressed  to  the  British  Association. 
Same  title,  four  pages,  addressed  to  M.  Mathieu.  Same  title,  four 
pages,  on  M.  Bouvard's  report. — Resume  de  la  physique  de  la  crea- 
tion ;  troisieme  partie  du  vrai  systeme  du  monde. 

The  quadrature  of  the  circle  discovered,  by  Arthur  Parsey,  author 
of  the  'art  of  miniature  painting.'  Submitted  to  the  consider- 
ation of  the  Royal  Society,  on  whose  protection  the  author 
humbly  throws  himself.  London,  1832,  8vo. 

Mr. .Parsey  was  an  artist,  who  also  made  himself  conspicuous 
by  a  new  view  of  perspective.  Seeing  that  the  sides  of  a  tower, 
for  instance,  would  appear  to  meet  in  a  point  if  the  tower  were 
high  enough,  he  thought  that  these  sides  ought  to  slope  to  one 
another  in  the  picture.  On  this  theory  he  published  a  small 
work,  of  which  I  have  not  the  title,  with  a  Grecian  temple  in  the 
frontispiece,  stated,  if  I  remember  rightly,  to  be  the  first  picture 
which  had  ever  been  drawn  in  true  perspective.  Of  course  the 
building  looked  very  Egyptian,  with  its  sloping  sides.  The 
answer  to  his  notion  is  easy  enough.  What  is  called  the  picture 
is  not  the  picture  from  which  the  mind  takes  its  perception ;  that 
picture  is  on  the  retina.  The  intermediate  picture,  as  it  may  be 
called — the  human  artist's  work — is  itself  seen  perspectively.  If 


PERSPECTIVE — RITCHIE'S   GEOMETRY.  177 

the  tower  were  so  high  that  the  sides,  though  parallel,  appeared 
to  meet  in  a  point,  the  picture  must  also  be  so  high  that  the 
picture-sides,  though  parallel,  would  appear  to  meet  in  a  point. 
I  never  saw  this  answer  given,  though  I  have  seen  and  heard  the 
remarks  of  artists  on  Mr.  Parsey's  work.  I  am  inclined  to  think 
it  is  commonly  supposed  that  the  artist's  picture  is  the  represen- 
tation which  comes  before  the  mind :  this  is  not  true  ;  we  might 
as  well  say  the  same  of  the  object  itself.  In  July  1831,  reading 
an  article  on  squaring  the  circle,  and  finding  that  there  was  a 
difficulty,  he  set  to  work,  got  a  light  denied  to  all  the  mathe- 
maticians in — some  would  say  through — a  crack,  and  advertised 
in  the  Times  that  he  had  done  the  trick.  He  then  prepared  this 
work,  in  which,  those  who  read  it  will  see  how,  he  showed  that 

3*14159 should  be  3-0625.     He  might  have  found  out  his 

error  by  stepping  a  draughtsman's  circle  with  the  compasses. 

Perspective  has  not  had  many  paradoxes.  The  only  other  one 
I  remember  is  that  of  a  writer  on  perspective,  whose  -name  I 
forget,  and  whose  four  pages  I  do  not  possess.  He  circulated 
remarks  on  my  notes  on  the  subject,  published  in  the  Athencewm*, 
in  which  he  denies  that  the  stereographic  projection  is'  a  case  of 
perspective,  the  reason  being  that  the  whole  hemisphere  makes 
too  large  a  picture  for  the  eye  conveniently  to  grasp  at  once. 
That  is  to  say,  it  is  no  perspective  because  there  is  too  much 
perspective. 

Principles  of  Geometry  familiarly  illustrated.     By  the  Rev.  W. 

Ritchie,  LL.D.     London,  1833,  12mo. 
A  new  Exposition  of  the  system  of  Euclid's  Elements,  being  an 

attempt  to  establish  his  work  on  a  different  basis.     By  Alfred 

Day,  LL.D.     London,  1839,  12mo. 

These  works  belong  to  a  small  class  which  have  the  peculiarity 
of  insisting  that  in  the  general  propositions  of  geometry  a  propo- 
sition gives  its  converse :  that  'Every  B  is  A'  follows  from  'Every 
A  is  B.'  Dr.  Ritchie  says,  '  If  it  be  proved  that  the  equality  of 
two  of  the  angles  of  a  triangle  depends  essentially  upon  the 
equality  of  the  opposite  sides,  it  follows  that  the  equality  of  the 
opposite  sides  depends  essentially  on  the  equality  of  the  angles.' 
Dr.  Day  puts  it  as  follows  : — 

'  That  the  converses  of  Euclid,  so  called,  where  no  particular  limit- 
ation is  specified  or  implied  in  the  leading  proposition,  more  than  in 
the  converse,  must  be  necessarily  true ;  for  as  by  the  nature  of  the 
reasoning  the  leading  proposition  must  be  universally  true,  should  the 
converse  not  be  so,  it  cannot  be  so  universally,  but  has  uu  lea^t  all  tho 

N 


178  A  BUDGET  OF  PAKADOXES. 

exceptions  conveyed  in  the  leading  proposition,  and  the  case  is  therefore 
unadapted  to  geometric  reasoning  ;  or,  what  is  the  same  thing,  by  the 
very  nature  of  geometric  reasoning,  the  particular  exceptions  to  the 
extended  converse  must  be  identical  with  some  one  or  other  of  the 
cases  under  the  universal  affirmative  proposition  with  which  we  set 
forth,  which  is  absurd.' 

On  this  I  cannot  help  transferring  to  my  reader  the  words  of  the 
Pacha  when  he  orders  the  bastinado, — May  it  do  you  good !  A 
rational  study  of  logic  is  much  wanted  to  show  many  mathema- 
ticians, of  all  degrees  of  proficiency,  that  there  is  nothing  in  the 
reasoning  of  mathematics  which  differs  from  other  reasoning. 
Dr.  Day  repeated  his  argument  in  '  A  Treatise  on  Proportion/ 
London,  1840,  8vo.  Dr.  Ritchie  was  a  very  clear-headed  man. 
He  published,  in  1818,  a  work  on  arithmetic,  with  rational  ex- 
planations. This  was  too  early  for  such  an  improvement,  and 
nearly  the  whole  of  this  excellent  work  was  sold  as  waste  paper. 
His  elementary  introduction  to  the  Differential  Calculus  was 
drawn  up  while  he  was  learning  the  subject  late  in  life.  Books 
of  this  sort  are  often  very  effective  on  points  of  difficulty. 


Letter  to  the  Royal  Astronomical  Society  in  refutation  of  Mistaken 
Notions  held  in  common,  by  the  Society,  and  by  all  the  New- 
tonian philosophers.  By  Capt.  Forman,  R.N.  Shepton- Mallet, 
1833,  8vo. 

Capt.  Forman  wrote  against  the  whole  system  of  gravitation, 
and  got  no  notice.  He  then  wrote  to  Lord  Brougham,  Sir  J. 
Herschel,  and  others  I  suppose,  desiring  them  to  procure  notice 
of  his  books  in  the  reviews :  this  not  being  acceded  to,  he  wrote 
(in  print)  to  Lord  John  Russell  to  complain  of  their  '  dishonest ' 
conduct.  He  then  sent  a  manuscript  letter  to  the  Astronomical 
Society,  inviting  controversy :  he  was  answered  by  a  recommen- 
dation to  study  dynamics.  The  above  pamphlet  was  the  con- 
sequence, in  which,  calling  the  Council  of  the  Society  '  craven 
dunghill  cocks,'  he  set  them  right  about  their  doctrines.  From 
all  I  can  learn,  the  life  of  a  worthy  man  and  a  creditable  officer 
was  completely  embittered  by  his  want  of  power  to  see  that  no 
person  is  bound  in  reason  to  enter  into  controversy  with  every 
one  who  chooses  to  invite  him  to  the  field.  This  mistake  is  not 
peculiar  to  philosophers,  whether  of  orthodoxy  or  paradoxy;  a 
majority  of  educated  persons  imply,  by  their  modes  of  proceeding, 
that  no  one  has  a  right  to  any  opinion  which  he  is  not  prepared 
to  defend  against  all  comers. 


INSPIRED  PARADOXERS.  179 


David  and  Goliath,  or  an  attempt  to  prove  that  the  Newtonian 
system  of  Astronomy  is  directly  opposed  to  the  Scriptures. 
By  Wm.  Lauder,  Sen.,  Mere,  Wilts.  Mere,  1833,  12mo. 

Newton  is  Goliath;  Mr.  Lauder  is  David.  David  took  five 
pebbles ;  Mr.  Lauder  takes  five  arguments.  He  expects  oppo- 
sition ;  for  Paul  and  Jesus  both  met  with  it. 

Mr.  Lauder,  in  his  comparison,  seems  to  put  himself  in  the 
divinely  inspired  class.  This  would  not  be  a  fair  inference  in 
every  case  ;  but  we  know  not  what  to  think  when  we  remember 
that  a  tolerable  number  of  cyclometers  have  attributed  their 
knowledge  to  direct  revelation.  The  works  of  this  class  are  very 
scarce  ;  I  can  only  mention  one  or  two  from  Montucla.  Alphonso 
Cano  de  Molina,  in  the  last  century,  upset  all  Euclid,  ani  squared 
the  circle  upon  the  ruins;  he  found  a  follower,  Janson,  who 
translated  him  from  Spanish  into  Latin.  He  declared  that  he 
believed  in  Euclid,  until  God,  who  humbles  the  proud,  taught 
him  better.  One  Paul  Yvon,  called  from  his  estate  de  la  Leu, 
a  merchant  at  Eochelle,  supported  by  his  book-keeper,  M.  Pujos, 
and  a  Scotchman,  John  Dunbar,  solved  the  problem  by  divine 
grace,  in  a  manner  which  was  to  convert  all  Jews,  Infidels,  &c. 
There  seem  to  have  been  editions  of  his  work  in  1619  and  1628, 
and  a  controversial  'Examen'  in  1630,  by  Eobert  Sara.  There 
was  a  noted  discussion,  in  which  Mydorge,  Hardy,  and  others 
took  part  against  de  la  Leu.  I  cannot  find  this  name  either  in 
Lipenius  or  Murhard,  and  I  should  not  have  known  the  dates  if 
it  had  not  been  for  one  of  the  keenest  bibliographers  of  any  time, 
my  friend  Prince  Balthasar  Boncompagni,  who  is  trying  to  find 
copies  of  the  works,  and  has  managed  to  find  copies  of  the  titles. 
In  1750,  Henry  Sullamar,  an  Englishman,  squared  the  circle  by 
the  number  of  the  Beast :  he  published  a  pamphlet  every  two  or 
three  years ;  but  I  cannot  find  any  mention  of  him  in  English 
works.  In  France,  in  1753,  M.  de  Causans,  of  the  Guards,  cut  a 
circular  piece  of  turf,  squared  it,  and  deduced  original  sin  and 
the  Trinity.  He  found  out  that  the  circle  was  equal  to  the 
square  in  which  it  is  inscribed ;  and  he  offered  a  reward  for 
detection  of  any  error,  and  actually  deposited  10,000  francs  as 
earnest  of  300,000.  But  the  courts  would  not  allow  any  one  to 
recover. 

1834.  In  this  year  Sir  John  Herschel  set  up  his  telescope  at 
Feldhausen,  Cape  of  Good  Hope.  He  did  much  for  astronomy, 

N    2 


180  A  BUDGET  OF  PARADOXES. 

but  not  much  for  the  Budget  of  Paradoxes.  He  gives  me,  how- 
ever, the  following  story.  He  showed  a  resident  a  remarkable 
blood-red  star,  and  some  little  time  after  he  heard  of  a  sermon 
preached  in  those  parts  in  which  it  was  asserted  that  the  state- 
ments of  the  Bible  must  be  true,  for  that  Sir  J.  H.  had  seen  in  his 
telescope  '  the  very  place  where  wicked  people  go.' 

But  red  is  not  always  the  colour.  Sir  J.  Herschel  has  in  his 
possession  a  letter  written  to  his  father,  Sir  W.  H.,  dated  April 
3,  1787,  and  signed  '  Eliza  Cumyns,'  begging  to  know  if  any  of 
the  stars  be  indigo  in  colour,  '  because,  if  there  be,  I  think  it 
may  be  deemed  a  strong  conjectural  illustration  of  the  expression, 
so  often  used  by  our  Saviour  in  the  Holy  Gospels,  that  "  the 
disobedient  shall  be  cast  into  outer  darkness  ;  "  for  as  the  Almighty 
Being  can  doubtless  confine  any  of  his  creatures,  whether  cor- 
poreal or  spiritual,  to  what  part  of  his  creation  He  pleases,  if 
therefore  any  of  the  stars  (which  are  beyond  all  doubt  so  many 
suns  to  other  systems)  be  of  so  dark  a  colour  as  that  above 
mentioned,  they  may  be  calculated  to  give  the  most  insufferable 
heat  to  those  dolorous  systems  dependent  upon  them  (and  to 
reprobate  spirits  placed  there),  without  one  ray  of  cheerful  light ; 
and  may  therefore  be  the  scenes  of  future  punishments.'  This 
letter  is  addressed  to  Dr.  Heirschel  at  Slow.  Some  have  placed 
the  infernal  regions  inside  the  earth,  but  others  have  filled  this 
internal  cavity — for  cavity  they  will  have — with  refulgent  light, 
and  made  it  the  abode  of  the  blessed.  It  is  difficult  to  build 
without  knowing  the  number  to  be  provided  for.  A  friend  of 
mine  heard  the  following  (part)  dialogue  between  two  strong 
Scotch  Calvinists :  '  Noo !  hoo  manny  d'ye  thank  there  are  of 
the  alact  on  the  arth  at  this  moment  ?— Eh  I  mabbee  a  doozen — 
Hoot !  mon !  nae  so  mony  as  thot  1 ' 

1834.  From  1769  to  1834  the  Nautical  Almanac  was  pub- 
lished on  a  plan  which  gradually  fell  behind  what  was  wanted. 
In  1834  the  new  series  began,  under  a  new  superintendent  (Lieut. 
"W.  S.  Stratford).  There  had  been  a  long  scientific  controversy, 
which  would  not  be  generally  intelligible.  To  set  some  of  the 
points  before  the  reader,  I  reprint  a  cutting  which  I  have  by  me. 
It  is  from  the  Nautical  Magazine,  but  I  did  hear  that  some  had 
an  idea  that  it  was  in  the  Nautical  Almanac  itself.  It  certainly 
was  not,  and  I  feel  satisfied  the  Lords  of  the  Admiralty  would 
not  have  permitted  the  insertion  ;  they  are  never  in  advance  of 
their  age.  The  Almanac  for  1834  was  published  in  July  1833. 


COUNCIL  OF  THE  SOLAR  SYSTEM.  181 


THE  NEW   NAUTICAL  ALMANAC. — Extract  from  the  'Primum  Mobile,' 
and  '  Milky  Way  Gazette.'     Communicated  by  AEROLITE. 

A  meeting  of  the  different  bodies  composing  the  Solar  System 
was  this  day  held  at  the  Dragon's  Tail,  for  the  purpose  of  taking 
into  consideration  the  alterations  and  amendments  introduced 
into  the  New  Nautical  Almanac.  The  honourable  luminaries 
had  been  individually  summoned  by  fast-sailing  comets,  and 
there  was  a  remarkably  full  attendance.  Among  the  visitors  we 
observed  several  nebulas,  and  almost  all  the  stars  whose  proper 
motions  would  admit  of  their  being  present. 

The  SUN  was  unanimously  called  to  the  focus.  The  small 
planets  took  the  oaths,  and  their  places,  after  a  short  discussion, 
in  which  it  was  decided  that  the  places  should  be  those  of  the 
Almanac  itself,  with  leave  reserved  to  move  for  corrections. 

Petitions  were  presented  from  a  and  8  Ursae  Minoris,  com- 
plaining of  being  put  on  daily  duty,  and  praying  for  an  increase  of 
salary. — Laid  on  the  plane  of  the  ecliptic. 

The  trustees  of  the  eccentricity1  and  inclination  funds  re- 
ported a  balance  of  '00001  in  the  former,  and  a  deficit  of  0"'009 
in  the  latter.  This  announcement  caused  considerable  surprise, 
and  a  committee  was  moved  for,  to  ascertain  which  of  the  bodies 
had  more  or  less  than  his  share.  After  some  discussion,  in 
which  the  small  planets  offered  to  consent  to  a  reduction,  if 
necessary,  the  motion  was  carried. 

The  FOCAL  BODY  then  rose  to  address  the  meeting.  He  re- 
marked that  the  subject  on  which  they  were  assembled  was  one 
of  great  importance  to  the  routes  and  revolutions  of  the  heavenly 
bodies.  For  himself,  though  a  private  arrangement  between  two 
of  his  honourable  neighbours  (here  he  looked  hard  at  the  Earth 
and  Venus)  had  prevented  his  hitherto  paying  that  close  atten- 
tion to  the  predictions  of  the  Nautical  Almanac  which  he  de- 
clared he  always  had  wished  to  do ;  yet  he  felt  consoled  by 
knowing  that  the  conductors  of  that  work  had  every  disposition 
to  take  his  peculiar  circumstances  into  consideration.  He  de- 
clared that  he  had  never  passed  the  wires  of  a  transit  without 
deeply  feeling  his  inability  to  adapt  himself  to  the  present  state 
of  his  theory ;  a  feeling  which  he  was  afraid  had  sometimes  caused 
a  slight  tremor  in  his  limb.  Before  he  sat  down,  he  expressed  a 
hope  that  honourable  luminaries  would  refrain  as  much  as 
possible  from  eclipsing  each  other,  or  causing  mutual  perturba- 

1  See  Sir  J.  Herschel's  Astronomy,  p.  369. 


182  A   BUDGET  OF  PARADOXES. 

tions.     Indeed,  he  should  be  very  sorry  to  see  any  interruption  of 
the  harmony  of  the  spheres.     (Applause.) 

The  several  articles  of  the  New  Nautical  Almanac  were  then 
read  over  without  any  comment ;  only  we  observed  that  Saturn 
shook  Ms  ring  at  every  novelty,  and  Jupiter  gave  his  belt  a 
hitch,  and  winked  at  the  satellites  at  page  21  of  each  month. 

The  MOON  rose,  to  propose  a  resolution.  No  one,  he  said, 
would  be  surprised  at  his  bringing  this  matter  forward  in  the 
way  he  did,  when  it  was  considered  in  how  complete  and  satis- 
factory a  manner  his  motions  were  now  represented.  He  must 
own  he  had  trembled  when  the  Lords  of  the  Admiralty  dissolved 
the  Board  of  Longitude,  but  his  tranquillity  was  more  than  re- 
established by  the  adoption  of  the  new  system.  He  did  not 
know  but  that  any  little  assistance  he  could  give  in  Nautical 
Astronomy  was  becoming  of  less  and  less  value  every  day,  owing 
to  the  improvement  of  chronometers.  But  there  was  one  thing, 
of  which  nothing  could  deprive  him — he  meant  the  regulation  of 
the  tides.  And,  perhaps,  when  his  attention  was  not  occupied  by 
more  than  the  latter,  he  should  be  able  to  introduce  a  little 
more  regularity  into  the  phenomena.  (Here  the  honourable 
luminary  gave  a  sort  of  modest  libration,  which  convulsed  the 
meeting  with  laughter.)  They  might  laugh  at  his  natural 
infirmity  if  they  pleased,  but  he  could  assure  them  it  arose  only 
from  the  necessity  he  was  under,  when  young,  of  watching  the 
motions  of  his  worthy  primary.  He  then  moved  a  resolution 
highly  laudatory  of  the  alterations  which  appeared  in  the  New 
Nautical  Almanac. 

The  EARTH  rose,  to  second  the  motion.  His  honourable  satel- 
lite had  fully  expressed  his  opinions  on  the  subject.  He  joined 
his  honourable  friend  in  the  focus  in  wishing  to  pay  every 
attention  to  the  Nautical  Almanac,  but,  really,  when  so  impor- 
tant an  alteration  had  taken  place  in  his  magnetic  pole l  (hear) 
and  there  might,  for  aught  he  knew,  be  a  successful  attempt  to 
reach  his  pole  of  rotation,  he  thought  he  could  not  answer  for 
the  preservation  of  the  precession  in  its  present  state.  (Here 
the  hon.  luminary,  scratching  his  side,  exclaimed,  as  he  sat  down, 
4  More  steam-boats — confound  'em !') 

An  honourable  satellite  (whose  name  we  could  not  learn)  pro- 
posed that  the  resolution  should  be  immediately  despatched,  cor- 
rected for  refraction,  when  he  was  called  to  order  by  the  Focal 
Body,  who  reminded  him  that  it  was  contrary  to  the  moving 

1  Captain  Ross  had  just  stuck  a  bit  of  brass  there. 


COUNCIL  OF  THE  SOLAR   SYSTEM.  183 

orders  of  the  system  to  take  cognizance  of  what  passed  inside  the 
atmosphere  of  any  planet. 

SATURN  and  PALLAS  rose  together.  (Cries  of  '  New  member  ! ' 
and  the  former  gave  way.)  The  latter,  in  a  long  and  eloquent 
speech,  praised  the  liberality  with  which  he  and  his  colleagues  had 
at  length  been  relieved  from  astronomical  disqualifications.  He 
thought  that  it  was  contrary  to  the  spirit  of  the  laws  of  gravita- 
tion to  exclude  any  planet  from  office  on  account  of  the  eccen- 
tricity or  inclination  of  his  orbit.  Honourable  luminaries  need 
not  talk  of  the  want  of  convergency  of  his  series.  What  had 
they  to  do  with  any  private  arrangements  between  him  and  the 
general  equations  of  the  system  ?  (Murmurs  from  the  opposi- 
tion.) So  long  as  he  obeyed  the  laws  of  motion,  to  which  he  had 
that  day  taken  a  solemn  oath,  he  would  ask,  were  old  planets, 
which  were  now  so  well  known  that  nobody  trusted  them, 
to  .... 

The  FOCAL  BODY  said  he  was  sorry  to  break  the  continuity  of 
the  proceedings,  but  he  thought  that  remarks  upon  character, 
with  a  negative  sign,  would  introduce  differences  of  too  high  an 
order.  The  honourable  luminary  must  eliminate  the  expression 
which  he  had  brought  out,  in  finite  terms,  and  use  smaller  in- 
equalities in  future.  (Hear,  hear.) 

PALLAS  explained,  that  he  was  far  from  meaning  to  reflect  upon 
the  orbital  character  of  any  planet  present.  He  only  meant  to 
protest  against  being  judged  by  any  laws  but  those  of  gravitation, 
and  the  differential  calculus:  he  thought  it  most  unjust  that 
astronomers  should  prevent  the  small  planets  from  being  ob- 
served, and  then  reproach  them  with  the  imperfections  of  the 
tables,  which  were  the  result  of  their  own  narrow-minded  policy. 
(Cheers. ) 

SATURN  thought  that,  as  an  old  planet,  he  had  not  been 
treated  with  due  respect.  (Hear,  from  his  satellites.)  He  had 
long  foretold  the  wreck  of  the  system  from  the  friends  of  inno- 
vation. Why,  he  might  ask,  were  his  satellites  to  be  excluded, 
when  small  planets,  trumpery  comets,  which  could  not  keep  their 
mean  distances  (cries  of  oh !  oh  !),  double  stars,  with  graphical 
approximations,  and  such  obscure  riff-raff  of  the  heavens  (great 
uproar)  found  room  enough.  So  help  him  Arithmetic,  nothing 
could  come  of  it,  but  a  stoppage  of  all  revolution.  His  hon. 
friend  in  the  focus  might  smile,  for  he  would  be  a  gainer  by  such 
an  event ;  but  as  for  him  (Saturn),  he  had  something  to  lose, 
and  hon.  luminaries  well  knew  that,  whatever  they  might  think 
under  an  atmosphere,  above  it  continual  revolution  was  the  only 


184  A   BUDGET   OF  PARADOXES. 

way  of  preventing  perpetual  anarchy.  As  to  the  hon.  luminary 
who  had  risen  before  him,  he  was  not  surprised  at  his  remarks, 
for  he  had  invariably  observed  that  he  and  bis  colleagues  allowed 
themselves  too  much  latitude.  The  stability  of  the  system  re- 
quired that  they  should  be  brought  down,  and  he,  for  one,  would 
exert  all  his  powers  of  attraction  to  accomplish  that  end.  If 
other  bodies  would  cordially  unite  with  him,  particularly  his 
noble  friend  next  him,  than  whom  no  luminary  possessed  greater 
weight — 

JUPITER  rose  to  order.  He  conceived  his  noble  friend  had  no 
right  to  allude  to  him  in  that  manner,  and  was  much  surprised  at 
his  proposal,  considering  the  matters  which  remained  in  dispute 
between  them.  In  the  present  state  of  affairs,  he  would  take 
care  never  to  be  in  conjunction  with  his  hon.  neighbour  one 
moment  longer  than  he  could  help.  (Cries  of  '  Order,  order,  no 
long  inequalities,'  during  which  he  sat  down.) 

SATURN  proceeded  to  say,  that  he  did  not  know  till  then  that  a 
planet  with  a  ring  could  affront  one  who  had  only  a  belt,  by  pro- 
posing mutual  co-operation.  He  would  now  come  to  the  subject 
under  discussion.  He  should  think  meanly  of  his  hon.  col- 
leagues if  they  consented  to  bestow  their  approbation  upon  a 
mere  astronomical  production.  Had  they  forgotten  that  they 
once  were  considered  the  arbiters  of  fate,  and  the  prognosticators 
of  man's  destiny  ?  What  had  lost  them  that  proud  position  ? 
Was  it  not  the  infernal  march  of  intellect,  which,  after  having 
turned  the  earth  topsy-turvy,  was  now  disturbing  the  very 
universe.  For  himself  (others  might  do  as  they  pleased),  but  he 
stuck  to  the  venerable  Partridge,  and  the  Stationers'  Company, 
and  trusted  that  they  would  outlive  infidels  and  anarchists,  whether 
of  Astronomical  or  Diffusion  of  Knowledge  Societies.  (Cries  of 
oh!  oh!) 

MARS  said  he  had  been  told,  for  he  must  confess  he  had  not 
seen  the  work,  that  the  places  of  the  planets  were  given  for 
Sundays.  This,  he  must  be  allowed  to  say,  was  an  indecorum 
he  had  not  expected ;  and  he  was  convinced  the  Lords  of  the 
Admiralty  had  given  no  orders  to  that  effect.  He  hoped  this 
point  would  be  considered  in  the  measure  which  had  been  intro- 
duced in  another  place,  and  that  some  one  would  move  that  the 
prohibition  against  travelling  on  Sundays  extend  to  the  heavenly 
as  well  as  earthly  bodies. 

Several  of  the  stars  here  declared,  that  they  had  been  much 
annoyed  by  being  observed  on  Sunday  evenings,  during  the  hours 
of  divine  service. 


COUNCIL   OF   THE   SOLAE   SYSTEM.  185 

The  room  was  then  cleared  for  a  division,  but  we  are  unable  to 
state  what  took  place.  Several  comets-at-arms  were  sent  for,  and 
we  heard  rumours  of  a  personal  collision  having  taken  place 
between  two  luminaries  in  opposition.  We  were  afterwards  told, 
that  the  resolution  was  carried  by  a  majority,  and  the  luminaries 
elongated  at  2  h.  15  m.  33,41  s.  sidereal  time. 


*  * 
* 


It  is  reported,  but  we  hope  without  foundation,  that 
Saturn,  and  several  other  discontented  planets,  have  accepted  an 
invitation  from  Sirius  to  join  his  system,  on  the  most  liberal 
appointments.  We  believe  the  report  to  have  originated  in 
nothing  more  than  the  discovery  of  the  annual  parallax  of  Sirius 
from  the  orbit  of  Saturn  ;  but  we  may  safely  assure  our  readers 
that  no  steps  have  as  yet  been  taken  to  open  any  communica- 
tion. 

We  are  also  happy  to  state,  that  there  is  no  truth  in  the 
rumour  of  the  laws  of  gravitation  being  about  to  be  repealed. 
We  have  traced  this  report,  and  find  it  originated  with  a  gentle- 
man living  near  Bath  (Captain  Forman,  E.N.),  whose  name  we 
forbear  to  mention. 

A  great  excitement  has  been  observed  among  the  nebulae, 
visible  to  the  earth's  southern  hemisphere,  particularly  among 
those  which  have  not  yet  been  discovered  from  thence.  We  are 
at  a  loss  to  conjecture  the  cause,  but  we  shall  not  fail  to  report 
to  our  readers  the  news  of  any  movement  which  may  take  place. 
(Sir  J.  Herschel's  visit.  He  could  just  see  this  before  he  went 
out.) 

A  Treatise  on  the  Divine  System  of  the  Universe,  by  Captain 
Woodley,  B.N.,  and  as  demonstrated  by  his  Universal  Time- 
piece, and  universal  method  of  determining  a  ship's  longitude 
by  the  apparent  true  place  of  the  moon  ;  with  an  introduction 
refuting  the  solar  system  of  Copernicus,  the  Newtonian  philo- 
sophy, and  mathematics.  1834.  8vo. 

Description  of  the  Universal  Time-piece.     (4  pp.  12mo.) 

I  think  this  divine  system  was  published  several  years  before, 
and  was  republished  with  an  introduction  in  1834.  Capt. 
Woodley  was  very  sure  that  the  earth  does  not  move :  he  pointed 
out  to  me,  in  a  conversation  I  had  with  him,  something — I  forget 
what — in  the  motion  of  the  Great  Bear,  visible  to  any  eye,  which 
could  not  possibly  be  if  the  earth  moved.  He  was  exceedingly 
ignorant,  as  the  following  quotation  from  his  account  of  the  usual 
opinion  will  show  : — 


186  A   BUDGET   OF   PARADOXES. 

The  north  pole  of  the  Earth's  axis  deserts,  they  say,  the  north  star 
or  pole  of  the  Heavens,  at  the  rate  of  1°  in  71|  years  .  .  .  The  fact  is, 
nothing  can  be  more  certain  than  that  the  Stars  have  not  changed 
their  latitudes  or  decimations  one  degree  in  the  last  71  f  years. 

This  is  a  strong  specimen  of  a  class  of  men  by  whom  all  ac- 
cessible persons  who  have  made  any  name  in  science  are  hunted. 
It  is  a  pity  that  they  cannot  be  admitted  into  scientific  societies, 
and  allowed  fairly  to  state  their  cases,  and  stand  quiet  cross- 
examination,  being  kept  in  their  answers  very  close  to  the 
questions,  and  the  answers  written  down.  I  am  perfectly  satisfied 
that  if  one  meeting  in  the  year  were  devoted  to  the  hearing  of 
those  who  chose  to  come  forward  on  such  conditions,  much  good 
would  be  done.  But  I  strongly  suspect  few  would  come  forward 
at  first,  and  none  in  a  little  while  :  and  I  have  had  some  ex- 
perience of  the  method  I  recommend,  privately  tried.  Capt. 
Woodley  was  proposed,  a  little  after  1834,  as  a  Fellow  of  the 
Astronomical  Society ;  and,  not  caring  whether  he  moved  the  sun 
or  the  earth,  or  both — I  could  not  have  stood  neither — I  signed 
the  proposal.  I  always  had  a  sneaking  kindness  for  paradoxers, 
such  a  one,  perhaps,  as  Petit  Andre  had  for  his  lambs,  as  he  called 
them.  There  was  so  little  feeling  against  his  opinions,  that  he 
only  failed  by  a  fraction  of  a  ball.  Had  I  myself  voted,  he  would 
have  been  elected ;  but  being  engaged  in  conversation,  and  not 
having  heard  the  slightest  objection  to  him,  I  did  not  think  it 
worth  while  to  cross  the  room  for  the  purpose.  I  regretted  this 
at  the  time,  but  had  I  known  how  ignorant  he  was  I  should  not 
have  supported  him.  Probably  those  who  voted  against  him 
knew  more  of  his  books  than  I  then  did. 

I  remember  no  other  instance  of  exclusion  from  a  scientific 
society  on  the  ground  of  opinion,  eves,  if  this  be  one  ;  of  which  it 
may  be  that  ignorance  had  more  to  do  with  it  than  paradoxy. 
Mr.  Frend,  a  strong  anti-Newtonian,  was  a  Fellow  of  the  Astro- 
nomical Society,  and  for  some  years  in  the  Council.  Lieut. 
Kerigan  was  elected  to  the  Eoyal  Society  at  a  time  when  his 
proposers  must  have  known  that  his  immediate  object  was  to  put 
F.E.S.  on  the  title-page  of  a  work  against  the  tides.  To  give  all 
I  know,  I  may  add  that  the  editor  of  some  very  ignorant  bombast 
about  the  '  forehead  of  the  solar  sky,:  who  did  not  know  the 
difference  between  Bailly  and  Baily,  received  hints  which  induced 
him  to  withdraw  his  proposal  for  election  into  the  Astronomical 
Society.  But  this  was  an  act  of  kindness ;  for  if  he  had  seen  Mr. 
Baily  in  the  chair,  with  his  head  on,  he  might  have  been  political 
historian  enough  to  faint  away. 


FRANCIS  BAILY  —  FLAMSTEED.  187 


De  la  formation  des  Corps.     Par  Paul  Laurent.    Nancy,  1834,  8vo. 

Atoms,  and  ether,  and  ovules  or  eggs,  which  are  planets,  and 
their  eggs,  which  are  satellites.  These  speculators  can  create 
worlds,  in  which  they  cannot  be  refuted  ;  but  none  of  them  dare 
attack  the  problem  of  a  grain  of  wheat,  and  its  passage  from  a 
seed  to  a  plant,  bearing  scores  of  seeds  like  what  it  was  itself. 

An  account  of  the  Rev.  John  Flamsteed,  the  First  Astronomer- 
Royal  ...  By  Francis  Baily,  Esq.  London,  1835,  4to.  Supple- 
ment, London,  1837,  4to. 

My  friend  Francis  Baily  was  a  paradoxer :  he  brought  forward 
things  counter  to  universal  opinion.  That  Newton  was  impeccable 
in  every  point  was  the  national  creed ;  and  failings  of  temper  and 
conduct  would  have  been  utterly  disbelieved,  if  the  paradox  had 
not  come  supported  by  very  unusual  evidence.  Anybody  who 
impeached  Newton  on  existing  evidence  might  as  well  have  been 
squaring  the  circle,  for  any  attention  he  would  have  got.  About 
this  book  I  will  tell  a  story.  It  was  published  by  the  Admiralty 
for  distribution  ;  and  the  distribution  was  entrusted  to  Mr.  Baily. 
On  the  eve  of  its  appearance,  rumours  of  its  extraordinary  reve- 
lations got  about,  and  persons  of  influence  applied  to  the  Admiralty 
for  copies.  The  Lords  were  in  a  difficulty :  but  on  looking  at 
the  list  they  saw  names,  as  they  thought,  which  were  so  obscure 
that  they  had  a  right  to  assume  Mr.  Baily  had  included  persons 
who  had  no  claim  to  such  a  compliment  as  presentation  from  the 
Admiralty.  The  Secretary  requested  Mr.  Baily  to  call  upon  him. 
'Mr.  Baily,  my  Lords  are  inclined  to  think  that  some  of  the 
persons  in  this  list  are  perhaps  not  of  that  note  which  would 
justify  their  Lordships  in  presenting  this  work.' — '  To  whom  does 
your  observation  apply,  Mr.  Secretary  ? ' — '  Well,  now,  let  us 
examine  the  list ;  let  me  see ;  now, — now, — now, — come  I — here's 
Gauss — who's  Gauss  ?  ' — '  Gauss,  Mr.  Secretary,  is  the  oldest 
mathematician  now  living,  and  is  generally  thought  to  be  the 
greatest.' — '  0-o-oh  !  Well,  Mr.  Baily,  we  will  see  about  it,  and  I 
will  write  you  a  letter.'  The  letter  expressed  their  Lordships' 
perfect  satisfaction  with  the  list. 

There  was  a  controversy  about  the  revelations  made  in  this 
work ;  but  as  the  eccentric  anomalies  took  no  part  in  it,  there  is 
nothing  for  my  purpose.  The  following  valentine  from  Mrs. 
Flamsteed,  which  I  found  among  Baily's  papers,  illustrates  some 
of  the  points  : — 


188  A   BUDGET  OF  PAEADOXES. 


'3  Astronomers'  Row,  Paradise :  February  14,  1836. 

*  Dear  Sir, — I  suppose  you  hardly  expected  to  receive  a  letter  from 
me,  dated  from  this  place  ;  but  the  truth  is,  a  gentleman  from  our 
street  was  appointed  guardian  angel  to  the  American  Treaty,  in  which 
there  is  some  astronomical  question  about  boundaries.  He  has  got 
leave  to  go  back  to  fetch  some  instruments  which  he  left  behind,  and 
I  take  this  opportunity  of  making  your  acquaintance.  That  America 
has  become  a  wonderful  place  since  I  was  down  among  you  ;  you  have 
no  idea  how  grand  the  fire  at  New  York  looked  up  here.  Poor  dear 
Mr.  Flamsteed  does  not  know  I  am  writing  a  letter  to  a  gentleman  on 
Valentine's  day ;  he  is  walked  out  with  Sir  Isaac  Newton  (they  are 
pretty  good  friends  now,  though  they  do  squabble  a  little  sometimes) 
and  Sir  William  Herschel,  to  see  a  new  nebula.  Sir  Isaac  says  he 
can't  make  out  at  all  how  it  is  managed ;  and  I  am  sure  I  cannot  help 
him.  I  never  bothered  my  head  about  those  things  down  below,  and 
I  don't  intend  to  begin  here. 

I  have  just  received  the  news  of  your  having  written  a  book  about 
my  poor  dear  man.  It's  a  chance  that  I  heard  it  at  all ;  for  the  truth 
is,  the  scientific  gentlemen  are  somehow  or  other  become  so  wicked, 
and  go  so  little  to  church,  that  very  few  of  them  are  considered  fit 
company  for  this  place.  If  it  had  not  been  for  Dr.  Brinkley,  who 
came  here  of  course,  I  should  not  have  heard  about  it.  He  seems  a 
nice  man,  but  is  not  yet  used  to  our  ways.  As  to  Mr.  Halley,  he  is  of 
course  not  here  ;  which  is  lucky  for  him,  for  Mr.  Flamsteed  swore  the 
moment  he  caught  him  in  a  place  where  there  are  no  magistrates,  he 
would  make  a  sacrifice  of  him  to  heavenly  truth.  It  was  very  generous 
in  Mr.  F.  not  appearing  against  Sir  Isaac  when  he  came  up,  for  I  am 
told  that  if  he  had,  Sir  Isaac  would  not  have  been  allowed  to  come  in 
at  all.  I  should  have  been  sorry  for  that,  for  he  is  a  companionable 
man  enough,  only  holds  his  head  rather  higher  than  he  should  do.  I 
met  him  the  other  pay  walking  with  Mr.  Whiston,  and  disputing  about 
the  deluge.  "  Well,  Mrs.  Flamsteed,"  says  he,  "  does  old  Poke-the- 
Stars  understand  gravitation  yet  ?  "  Now  you  must  know'that  is  rather 
a  sore  point  with  poor  dear  Mr.  Flamsteed.  He  says  that  Sir  Isaac  is 
as  crochetty  about  the  moon  as  ever  ;  and  as  to  what  some  people  say 
about  what  has  been  done  since  his  time,  he  says  he  should  like  to  see 
somebody  who  knows  something  about  it  of  himself.  For  it  is  very 
singular  that  none  of  the  people  who  have  carried  on  Sir  Isaac's  notions 
have  been  allowed  to  come  here. 

I  hope  you  have  not  forgotten  to  tell  how  badly  Sir  Isaac  used 
Mr.  Flamsteed  about  that  book.  I  have  never  quite  forgiven  him  ;  as 
for  Mr.  Flamsteed,  he  says  that  as  long  as  he  does  not  come  for  ob- 
servations, he  does  not  care  about  it,  and  that  he  will  never  trust  him 
with  any  papers  again  as  long  as  he  lives.  I  shall  never  forget  what 
a  rage  he  came  home  in  when  Sir  Isaac  had  called  him  a  puppy.  He 
struck  the  stairs  all  the  way  up  with  his  crutch,  and  said  puppy  at 


MRS.  FLAMSTE ED'S   VALENTINE.  189 

every  step,  and  all  the  evening,  as  soon  as  ever  a  star  appeared  in  the 
telescope,  he  called  it  puppy.  I  could  not  think  what  was  the  matter, 
and  when  I  asked,  he  only  called  me  puppy. 

I  shall  be  very  glad  to  see  you  if  you  come  our  way,  Pray  keep  up 
some  appearances,  and  go  to  church  a  little.  St.  Peter  is  always 
uncommonly  civil  to  astronomers,  and  indeed  to  all  scientific  persons, 
and  never  bothers  them  with  many  questions.  If  they  can  make  any- 
thing out  of  a  case,  he  is  sure  to  let  them  in.  Indeed,  he  says,  it  is 
perfectly  out  of  the  question  expecting  a  mathematician  to  be  as 
religious  as  an  apostle,  but  that  it  is  as  much  as  his  place  is  worth  to 
let  in  the  greater  number  of  those  who  come.  So  try  if  yon  cannot 
manage  it,  for  I  am  very  curious  to  know  whether  you  found  all  the 
letters.  I  remain,  dear  sir,  your  faithful  servant, 

MARGARET  FLAMSTEED. 

Francis  Baily,  Esq. 

P.S.  Mr.  Flamsteed  has  come  in,  and  says  he  left  Sir  Isaac  riding 
cockhorse  upon  the  nebula,  and  poring  over  it  as  if  it  were  a  book. 
He  has  brought  in  his  old  acquaintance  Ozanam,  who  says  that  it  was 
always  his  maxim  on  earth,  that  "  il  appartient  aux  docteurs  de 
Sorbonne  de  disputer,  au  Pape  de  prononcer,  et  au  mathematicien 
d'aller  en  Paradis  en  ligne  perpendiculaire." ' 

The  Secretary  of  the  Admiralty  was  completely  extinguished. 
I  can  recall  but  two  instances  of  demolition  as  complete,  though 
no  doubt  there  are  many  others.  The  first  is  in 

Simon  Stevin  and  M.  Dumortier.     Nieuport,  1845,  12mo. 

M.  Dumortier  was  a  member  of  the  Academy  of  Brussels  :  there 
was  a  discussion,  I  believe,  about  a  national  Pantheon  for  Bel- 
gium. The  name  of  Stevinus  suggested  itself  as  naturally  as 
that  of  Newton  to  an  Englishman  ;  probably  no  Belgian  is  better 
known  to  foreigners  as  illustrious  in  science.  Stevinus  is  great 
in  the  Mecanique  Analytique  of  Lagrange  ;  Stevinus  is  great  in 
the  Tristram,  Shandy  of  Sterne.  M.  Dumortier,  who  believed 
that  not  one  Belgian  in  a  thousand  knew  Stevinus,  and  who 
confesses  with  ironical  shame  that  he  was  not  the  odd  man, 
protested  against  placing  the  statue  of  an  obscure  man  in  the 
Pantheon,  to  give  foreigners  the  notion  that  Belgium  could  show 
nothing  greater.  Tbe  work  above  named  is  a  slashing  retort : 
any  one  who  knows  the  history  of  science  ever  so  little  may 
imagine  what  a  dressing  was  given,  by  mere  extract  from  foreign 
writers.  The  tract  is  a  letter  signed  J.  du  Fan,  but  this  is  a 
pseudonym  of  Mr.  Van  de  Weyer.  The  Academician  says 
Stevinus  was  a  man  who  was  not  without  merit  for  the  time  at 


190  A  BUDGET  OF  PARADOXES. 

which  he  lived :  Sir !  is  the  answer,  he  was  as  much  before  his 
own  time  as  you  are  behind  yours.  How  came  a  man  who 
had  never  heard  of  Stevinus  to  be  a  member  of  the  Brussels 
Academy  ? 

The  second  story  was  told  me  by  Mr.  Crabb  Eobinson,  who  was 
long  connected  with  the  Times,  and  intimately  acquainted  with 
Mr.  W***.  When  W***  was  an  undergraduate  at  Cambridge, 
taking  a  walk,  he  came  to  a  stile,  on  which  sat  a  bumpkin  who 
did  not  make  way  for  him :  the  gown  in  that  day  looked  down 
on  the  town.  '  Why  do  you  not  make  way  for  a  gentleman  ? ' 
— '  Eh  ? '  —  '  Yes,  why  do  you  not  move  ?  You  deserve  a  good 
hiding,  and  you  shall  get  it  if  you  don't  take  care  ? '  The 
bumpkin  raised  his  muscular  figure  on  its  feet,  patted  his 
menacer  on  the  head,  and  said,  very  quietly, — 'Young  man  !  I'm 
Cribb.'  W***  seized  the  great  pugilist's  hand,  and  shook  it 
warmly,  got  him  to  his  own  rooms  in  college,  collected  some 
friends,  and  had  a  symposium  which  lasted  until  the  large  end  of 
the  small  hours. 

God's  Creation  of  the  Universe  as  it  is,  in  support  of  the  Scriptures. 
By  Mr.  Finleyson.     Sixth  Edition,  1835,  8vo. 

This  writer,  by  his  own  account,  succeeded  in  delivering  the 
famous  Lieut.  Richard  Brothers  from  the  lunatic  asylum,  and 
tending  him,  not  as  a  keeper  but  as  a  disciple,  till  he  died. 
Brothers  was,  by  his  own  account,  the  nephew  of  the  Almighty, 
and  Finleyson  ought  to  have  been  the  nephew  of  Brothers.  For 
Napoleon  came  to  him  in  a  vision,  with  a  broken  sword  and  an 
arrow  in  his  side,  beseeching  help:  Finleyson  pulled  out  the 
arrow,  but  refused  to  give  a  new  sword ;  whereby  poor  Napoleon, 
though  he  got  off  with  life,  lost  the  battle  of  Waterloo.  This 
story  was  written  to  the  Duke  of  Wellington,  ending  with  '  I 
pulled  out  the  arrow,  but  left  the  broken  sword.  Your  Grace 
can  supply  the  rest,  and  what  followed  is  amply  recorded  in 
history.'  The  book  contains  a  long  account  of  applications  to 
Government  to  do  three  things  :  to  pay  2,000£.  for  care  taken  of 
Brothers,  to  pay  10,000£.  for  discovery  of  the  longitude,  and  to 
prohibit  the  teaching  of  the  Newtonian  system,  which  makes  God 
a  liar.  The  successive  administrations  were  threatened  that  they 
would  have  to  turn  out  if  they  refused,  which,  it  is  remarked, 
came  to  pass  in  every  case.  I  have  heard  of  a  joke  of  Lord 
Macaulay,  that  the  House  of  Commons  must  be  the  Beast  of  the 
Revelations,  since  658  members,  with  the  officers  necessary  for 
the  action  of  the  House,  make  666.  Macaulay  read  most  things, 


RICHARD   BROTHERS,   PROPHET   AND   POET.  101 

and  the  greater  part  of  the  rest :  so  that  he  might  be  suspected 
of  having  appropriated  as  a  joke  one  of  Finleyson's  serious  points 
— 'I  wrote  Earl  Grey  upon  the  13th  of  July,  1831,  informing 
him  that  his  Reform  Bill  could  not  be  carried,  as  it  reduced  the 
members  below  the  present  amount  of  658,  which,  with  the 
eight  principal  clerks  or  officers  of  the  House,  make  the  number 
666.'  But  a  witness  has  informed  me  that  Macaulay's  joke  was 
made  in  his  hearing  a  great  many  years  before  the  Reform  Bill 
was  proposed ;  in  fact,  when  both  were  students  at  Cambridge. 
Earl  Grey  was,  according  to  Finleyson,  a  descendant  of  Uriah 
the  Hittite.  For  a  specimen  of  Lieut.  Brothers,  this  book  would 
be  worth  picking  up.  Perhaps  a  specimen  of  the  Lieutenant's 
poetry  may  be  acceptable  :  Brothers  loquitur,  remember  : — 

Jerusalem  !  Jerusalem  !  shall  be  built  again  ! 

More  rich,  more  grand  than  ever  ; 
And  through  it  shall  Jordan  flow  !  (!) 

My  people's  favourite  river. 
There  I'll  erect  a  splendid  throne, 

And  build  on  the  wasted  place ; 
To  fulfil  my  ancient  covenant 

To  King  David  and  his  race. 
****** 

Euphrates'  stream  shall  flow  with  ships, 

And  also  my  wedded  Nile  ; 
And  on  my  coast  shall  cities  rise, 

Each  one  distant  but  a  mile. 

****** 

My  friends  the  Russians  on  the  north 

With  Persees  and  Arabs  round, 
Do  show  the  limits  of  my  land, 

Here  !  Here !  then  I  mark  the  ground. 

Among  the  paradoxers  are  some  of  the  theologians  who  in 
their  own  organs  of  the  press  venture  to  criticise  science.  These 
may  hold  their  ground  when  they  confine  themselves  to  the 
geology  of  long  past  periods  and  to  general  cosmogony  :  for  it  is 
the  tug  of  Greek  against  Greek ;  and  both  sides  deal  much  in 
what  is  grand  when  called  hypothesis,  petty  when  called  supposi- 
tion. And  very  often  they  are  not  conspicuous  when  they 
venture  upon  things  within  knowledge  ;  wrong,  but  not  quite 
wrong  enough  for  a  Budget  of  Paradoxes.  One  case,  however, 
is  destined  to  live,  as  an  instance  of  a  school  which  finds  writers, 
editors,  and  readers.  The  double  stars  have  been  seen  from  the 
seventeenth  century,  and  diligently  observed  by  many  from  the 


192  A  BUDGET  OF  PAEADOXES. 

time  of  Wm.  Herschel,  who  first  devoted  continuous  attention  to 
them.  The  year  1836  was  that  of  a  remarkable  triumph  of 
astronomical  prediction.  The  theory  of  gravitation  had  been 
applied  to  the  motion  of  binary  stars  about  each  other,  in  elliptic 
orbits,  and  in  that  year  the  two  stars  of  7  Virginis,  as  had  been 
predicted  should  happen  within  a  few  years  of  that  time — for 
years  are  small  quantities  in  such  long  revolutions — the  two 
stars  came  to  their  nearest :  in  fact,  they  appeared  to  be  one  as 
much  with  the  telescope  as  without  it.  This  remarkable  turn- 
ing-point of  the  history  of  a  long  and  widely-known  branch  of 
astronomy  was  followed  by  an  article  in  the  Church  of  England 
Quarterly  Review  for  April  1837,  written  against  the  Useful 
Knowledge  Society.  The  notion  that  there  are  any  such  things 
as  double  stars  is  (p.  460)  implied  to  be  imposture  or  delusion, 
as  in  the  following  extract.  I  suspect  that  I  myself  am  the 
Sidrophel,  and  that  my  companion  to  the  maps  of  the  stars, 
written  for  the  Society  and  published  in  1 836,  is  the  work  to 
which  the  writer  refers  : — 

We  have  forgotten  the  name  of  that  Sidrophel  who  lately  discovered 
that  the  fixed  stars  were  not  single  stars,  but  appear  in  the  heavens, 
like  soles  at  Billingsgate,  in  pairs ;  while  a  second  astronomer,  under 
the  influence  of  that  competition  in  trade  which  the  political  economists 
tell  us  is  so  advantageous  to  the  public,  professes  to  show  us,  through 
his  superior  telescope,  that  the  apparently  single  stars  are  really  three. 
Before  such  wondrous  mandarins  of  science,  how  continually  must 
homunculi  like  ourselves  keep  in  the  background,  lest  we  come  between 
the  wind  and  their  nobility. 

If  the  homunculus  who  wrote  this  be  still  above  ground,  how 
devoutly  must  he  hope  he  may  be  able  to  keep  in  the  back- 
ground !  But  the  chief  blame  falls  on  the  editor.  The  title  of 
the  article  is — 

The  new  school  of  superficial  pantology ;  a  speech  intended  to  be 
delivered  before  a  defunct  Mechanics'  Institute.  By  Swallow  Swift, 
late  M.P.  for  the  Borough,  of  Cockney- Cloud,  Witsbury :  reprinted 
Balloon  Island,  Bubble  year,  month  Ventose.  Long  live  Charlatan ! 

As  a  rule,  orthodox  theologians  should  avoid  humour,  a  weapon 
which  all  history  shows  to  be  very  difficult  to  employ  in  favour 
of  establishment,  and  which,  nine  times  out  of  ten,  leaves  its 
wielder  fighting  on  the  side  of  heterodoxy.  Theological  argu- 
ment, when  not  enlivened  by  bigotry,  is  seldom  worse  than 
narcotic  :  but  theological  fun,  when  not  covert  heresy,  is  almost 
always  sialagogue.  The  article  in  question  is  a  craze,  which  no 
editor  should  have  admitted,  except  after  severe  inspection  by 


SATIRICAL    CRITICISM.  193 

qualified  persons.  The  author  of  this  wit  committed  a  mistake 
which  occurs  now  and  then  in  old  satire,  the  confusion  between 
himself  and  the  party  aimed  at.  He  ought  to  be  reviewing  this 
fictitious  book,  but  every  now  and  then  the  article  becomes  the 
book  itself;  not  by  quotation,  but  by  the  writer  forgetting  that 
he  is  not  Mr.  Swallow  Swift,  but  his  reviewer.  In  fact,  he  and 
Mr.  S,  Swift  had  each  had  a  dose  of  the  Devil's  Elixir.  A  novel 
so  called,  published  about  forty  years  ago,  proceeds  upon  a 
legend  of  this  kind.  If  two  parties  both  drink  of  the  elixir, 
their  identities  get  curiously  intermingled  ;  each  turns  up  in 
the  character  of  the  other  throughout  the  three  volumes,  without 
having  his  ideas  clear  as  to  whether  he  be  himself  or  the  other. 
There  is  a  similar  confusion  in  the  answer  made  to  the  famous 
Epistolce  Obscurorum  Virorum:  it  is  headed  Lamentationes 
Obscurorum  Virorum.  This  is  not  a  retort  of  the  writer,  throw- 
ing back  the  imputation :  the  obscure  men  who  had  been 
satirized  are  themselves  made,  by  name,  to  wince  under  the 
disapprobation  which  the  Pope  had  expressed  at  the  satire  upon 
themselves. 

Of  course  the  book  here  reviewed  is  a  transparent  forgery. 
But  I  do  not  know  how  often  it  may  have  happened  that  the 
book,  in  the  journals  which  always  put  a  title  at  the  head,  may 
have  been  written  after  the  review.  About  the  year  1830  a 
friend  showed  me  the  proof  of  an  article  of  his  on  the  malt  tax, 
for  the  next  number  of  the  Edinburgh  Review.  Nothing  was 
wanting  except  the  title  of  the  book  reviewed ;  I  asked  what  it 
was.  He  sat  down,  and  wrote  as  follows  at  the  head,  '  The 
Maltster's  Guide  (pp.  124),'  and  said  that  would  do  as  well  as 
anything. 

But  I  myself,  it  will  be  remarked,  have  employed  such  humour 
as  I  can  command  'in  favour  of  establishment.'  What  it  is 
worth  I  am  not  to  judge ;  as  usual  in  such  cases,  those  who  are  of 
my  cabal  pronounce  it  good,  but  cyclometers  and  other  paradoxers 
either  call  it  very  poor,  or  commend  it  as  sheer  buffoonery.  Be 
it  one  or  the  other,  I  observe  that  all  the  effective  ridicule  is,  in 
this  subject,  on  the  side  of  establishment.  This  is  partly  due  to 
the  difficulty  of  quizzing  plain  and  sober  demonstration ;  but  so 
much,  if  not  more,  to  the  ignorance  of  the  paradoxers.  For  that 
which  cannot  be  ridiculed,  can  be  turned  into  ridicule  by  those 
who  know  how.  But  by  the  time  a  person  is  deep  enough  in 
negative  quantities,  and  impossible  quantities,  to  be  able  to  satirise 
them,  he  is^caught,  and  being  inclined  to  become  a  user,  sli rinks 
from  being  an  abuser.  Imagine  a  person  with  a  gift  of  ridicule, 

o 


194  A  BUDGET  OF  PARADOXES. 

and  knowledge  enough,  trying  his  hand  on  the  junction  of  the 
assertions  which  he  will  find  in  various  books  of  algebra.  First, 
that  a  negative  quantity  has  no  logarithm;  secondly,  that  a 
negative  quantity  has  no  square  root ;  thirdly,  that  the  first  non- 
existent is  to  the  second  as  the  circumference  of  a  circle  to  its 
diameter.  One  great  reason  of  the  allowance  of  such  unsound 
modes  of  expression  is  the  confidence  felt  by  the  writers  that  V— 1 
and  log  (-1)  will  make  their  way,  however  inaccurately  described. 
I  heartily  wish  that  the  cyclometers  had  knowledge  enough  to 
attack  the  weak  points  of  algebraical  diction  :  they  would  soon 
work  a  beneficial  change. 

Recueil  de  ma  vie,  mes  ouvrages  et  mes  pensees.     Par  Thomas 

Ignace  Marie  Forster.  Brussels,  1836,  12mo. 
Mr.  Forster,  an  Englishman  settled  at  Bruges,  was  an  observer 
in  many  subjects,  but  especially  in  meteorology.  He  communi- 
cated to  the  Astronomical  Society,  in  1848,  the  information  that, 
in  the  registers  kept  by  his  grandfather,  his  father,  and  himself, 
beginning  in  1767,  new  moon  on  Saturday  was  followed,  nineteen 
times  out  of  twenty,  by  twenty  days  of  rain  and  wind.  This 
statement  being  published  in  the  Athenceum,  a  cluster  of  corres- 
pondents averred  that  the  belief  is  common  among  seamen,  in  all 
parts  of  the  world,  and  among  landsmen  too.  Some  one  quoted 
a  distich — 

'  Saturday's  moon  and  Sunday's  full 
Never  were  fine  and  never  wull.' 
Another  brought  forward — 

'  If  a  Saturday's  moon 
Comes  once  in  seven  years  it  comes  too  soon.' 

Mr.  Forster  did  not  say  he  was  aware  of  the  proverbial  character 
of  the  phenomenon.  He  was  a  very  eccentric  man.  He  treated 
his  dogs  as  friends,  and  buried  them  with  ceremony.  He  quar- 
relled with  the  cure  of  his  parish,  who  remarked  that  he  could 
not  take  his  dogs  to  heaven  with  him.  I  will  go  nowhere,  said 
he,  where  I  cannot  take  my  dog.  He  was  a  sincere  Catholic :  but 
there  is  a  point  beyond  which  even  churches  have  no  influence. 

The  following  is  some  account  of  the  announcement  of  1849. 
The  Athenceum  (Feb.  17),  giving  an  account  of  the  meeting  of 
the  Astronomical  Society  in  December,  1858,  says: 

'  Dr.  Forster  of  Bruges,  who  is  well  known  as  a  meteorologist,  made 
a  communication  at  which  our  readers  will  stare  :  he  declares  that  by 
journals  of  the  weather  kept  by  his  grandfather,  father,  and  himself, 
ever  since  1767,  to  the  present  time,  whenever  the  new  moon  has  fallen 
on  a  Saturday i  the  following  twenty  days  have  been  wet  and  windy,  in 


A    SATURDAY'S    MOON.  195 

nineteen  cases  out  of  twenty.  In  spite  of  our  friend  Zadkiel  and  the 
others  who  declare  that  we  would  smother  every  truth  that  does  not 
happen  to  agree  with  us,  we  are  glad  to  see  that  the  Society  had 
the  sense  to  publish  this  communication,  coming,  as  it  does,  from  a 
veteran  observer,  and  one  whose  love  of  truth  is  undoubted.  It  must 
be  that  the  fact  is  so  set  down  in  the  journals,  because  Dr.  Forster 
says  it :  and  whether  it  be  only  a  fact  of  the  journals,  or  one  of  the 
heavens,  can  soon  be  tried.  The  new  moon  of  March  next,  falls  on 
Saturday  the  24th,  at  2  in  the  afternoon.  We  shall  certainly  look  out.' 

The  following  appeared  in  the  number  of  March  31  : — 

*  The  first  Saturday  Moon  since  Dr.  Forster's  announcement  came  off 
a  week  ago.  We  had  previously  received  a  number  of  letters  from 
different  correspondents — all  to  the  effect  that  the  notion  of  new  moon 
on  Saturday  bringing  wet  weather  is  one  of  widely  extended  currency. 
One  correspondent  (who  gives  his  name)  states  that  he  has  constantly 
heard  it  at  sea,  and  among  the  farmers  and  peasantry  in  Scotland, 
Ireland,  and  the  North  of  England.  He  proceeds  thus  :  "  Since  1826, 
nineteen  years  of  the  time  I  have  spent  in  a  seafaring  life.  I  have 
constantly  observed,  though  unable  to  account  for,  the  phenomenon. 
I  have  also  heard  the  stormy  qualities  of  a  Saturday's  moon  remarked 
by  American,  French,  and  Spanish  seamen  ;  and,  still  more  distant, 
a  Chinese  pilot,  who  was  once  doing  duty  on  board  my  vessel  seemed 
to  be  perfectly  cognizant  of  the  fact."  So  that  it  seems  we  have,  in 
giving  currency  to  what  we  only  knew  as  a  very  curious  communica- 
tion from  an  earnest  meteorologist,  been  repeating  what  is  common 
enough  among  sailors  and  farmers.  Another  correspondent  affirms 
that  the  thing  is  most  devoutly  believed  in  by  seamen  ;  who  would  as 
soon  sail  on  a  Friday  as  be  in  the  Channel  after  a  Saturday  moon. — 
After  a  tolerable  course  of  dry  weather,  there  was  some  snow,  accom- 
panied by  wind  on  Saturday  last,  here  in  London  ;  there  were  also 
heavy  louring  clouds.  Sunday  was  cloudy  and  cold,  with  a  little  rain  ; 
Monday  was  louring ;  Tuesday  unsettled ;  Wednesday  quite  over- 
clouded, with  rain  in  the  morning.  The  present  occasion  shows  only 
a  general  change  of  weather,  with  a  tendency  towards  rain.  If  Dr. 
Forster's  theory  be  true,  it  is  decidedly  one  of  the  minor  instances, 
as  far  as  London  weather  is  concerned. — It  will  take  a  good  deal  of 
evidence  to  make  us  believe  in  the  omen  of  a  Saturday  Moon.  But, 
as  we  have  said  of  the  Poughkeepsie  Seer,  the  thing  is  very  curious 
whether  true  or  false.  Whence  comes  this  universal  proverb — and  a 
hundred  others — while  the  meteorological  observer  cannot,  when  he 
puts  down  a  long  series  of  results,  detect  any  weather  cycles  at  all  ? 
One  of  our  correspondents  wrote  us  something  of  a  lecture  for  en- 
couraging, he  said,  the  notion  that  names  could  influence  the  weather. 
He  mistakes  the  question.  If  there  be  any  weather  cycles  depending 
on  the  moon,  it  is  possible  that  one  of  them  may  be  so  related  to  the 
k  cycle  of  seven  days,  as  to  show  recurrences  which  are  of  the  kind 

o  2 


196  A  BUDGET  OF  PARADOXES. 

stated,  or  any  other.  For  example,  we  know  that  if  the  new  moon  of 
March  fall  on  a  Saturday  iu  this  year,  it  will  most  probably  fall  on 
a  Saturday  nineteen  years  hence.  This  is  not  connected  with  the 
spelling  of  Saturday — but  with  the  connexion  between  the  motions  of 
the  sun  and  moon.  Nothing  but  the  Moon  can  settle  the  question — 
and  we  are  willing  to  wait  on  her  for  further  information.  If  the 
adage  be  true,  then  the  philosopher  has  missed  what  lies  before  his 
eyes ;  if  false,  then  the  world  can  be  led  by  the  nose  in  spite  of  the 
eyes.  Both  these  things  happen  sometimes;  and  we  are  willing  to 
take  whichever  of  the  two  solutions  is  borne  out  by  future  facts.  In 
the  mean  time,  we  announce  the  next  Saturday  Moon  for  the  18th 
of  August.' 

How  many  coincidences  are  required  to  establish  a  law  of 
connexion  ?  It  depends  on  the  way  in  which  the  mind  views  the 
matter  in  question.  Many  of  the  paradoxers  are  quite  set  up  by 
a  very  few  instances.  I  will  now  tell  a  story  about  myself,  and 
then  ask  them  a  question. 

So  far  as  instances  can  prove  a  law,  the  following  is  proved :  no 
failure  has  occurred.  Let  a  clergyman  be  known  to  me,  whether 
by  personal  acquaintance  or  correspondence,  or  by  being  frequently 
brought  before  me  by  those  with  whom  I  am  connected  in  private 
life :  that  clergyman  does  not,  except  in  few  cases,  become  a 
bishop ;  but,  if  he  become  a  bishop,  h<e  is  sure,  first  or  last,  to 
become  an  arch-bishop.  This  has  happened  in  every  case.  As 
follows : — 

1.  My  last  schoolmaster,  a  former  Fellow  of  Oriel,  was  a  very 
intimate   college   friend  of  Eichard    Whately,  a  younger  man. 
Struck  by  his  friend's  talents,  he  used  to  talk  of  him  perpetually, 
and   predict   his  future  eminence.      Before  I  was  sixteen,  and 
before  Whately  had  even  given  his  Barnpton  Lectures,  I  was  very 
familiar  with  his  name,  and  some  of  his  sayings.     I  need  not  say 
that  he  became  Archbishop  of  Dublin. 

2.  When  I  was  a  child,  a  first  cousin  of  John  Bird  Sumner 
married  a  sister  of  my  mother.     I  cannot  remember  the  time 
when  I  first  heard  his  name,  but  it  was  made  very  familiar  to  me. 
In  time  he  became  Bishop  of  Chester,  and  then,  Archbishop  of 
Canterbury.     My  reader  may  say  that  Dr.  C.  R.  Sumner,  Bishop 
of  Winchester,  has  just  as  good  a  claim  :  but  it  is  not  so  :  those 
connected  with  me  had  more  knowledge  of  Dr.  J.  B.   Sumner ; 
and  said  nothing,  or  next  to  nothing,  of  the  other.     Rumour  says 
that  the  Bishop  of  Winchester  has  declined  an  Archbishopric :  if 
so,  my  rule  is  a  rule  of  gradations. 

3.  Thomas  Musgrave,  Fellow   of  Trinity  College,  Cambridge, 
was  Dean  of  the  college  when  I  was  an  undergraduate  :    this 


ACCIDENT,  OR  LAW?  197 

brought  me  into  connexion  with  him,  he  giving  impositions  for 
not  going  to  chapel,  I  writing  them  out  according.  We  had 
also  friendly  intercourse  in  after  life ;  I  forgiving,  he  probably 
forgetting.  Honest  Tom  Musgrave,  as  he  used  to  be  called, 
became  Bishop  of  Hereford,  and  Archbishop  of  York. 

4.  About  the  time  when  I  went  to  Cambridge,  I  heard  a  great 
deal  about  Mr.  C.  T.  Longley,  of  Christchurch,   from  a  cousin 
of  my  own  of  the  same  college,  long  since  deceased,  who  spoke  of 
him  much,  and  most  affectionately.     Dr.  Longley  passed  from 
Durham  to  York,  and  thence  to  Canterbury.    I  cannot  quite  make 
out  the  two  Archbishoprics  ;  I  do  not  remember  any  other  private 
channel  through  which    the    name    came  to    me :    perhaps    Dr. 
Longley,  having  two  strings  to   his  bow,  would  have  been  one 
Archbishop  if  I  had  never  heard  of  him. 

5.  When  Dr.  Win.    Thomson   was   appointed   to    the   see    of 
Gloucester  in  1861,  he  and  I  had  been  correspondents  on  the 
subject  of  logic — on    which    we    had  both    written — for   about 
fourteen  years.     On  his  elevation  I  wrote  to  him,  giving  the  pre- 
ceding instances,  and  informing  him  that  he  would  certainly  be 
an  Archbishop.     The  case  was  a  strong  one,  and  the  law  acted 
rapidly;    for  Dr.  Thomson's  elevation  to  the   see  of  York  took 
place  in  1862. 

Here  are  five  cases ;  and  there  is  no  opposing  instance.  I  have 
searched  the  almanacs  since  1828,  and  can  find  no  instance  of  a 
Bishop  not  finally  Archbishop  of  whom  I  had  known  through 
private  sources,  direct  or  indirect.  Now  what  do  my  paradoxers 
say  ?  Is  this  a  pre-established  harmony,  or  a  chain  of  coinci- 
dences ?  And  how  many  instances  will  it  require  to  establish  a 
law? 

Some  account  of  the  great  astronomical  discoveries  lately  made 
by  Sir  John  Herschel  at  the  Cape  of  Good  Hope.  Second 
Edition.  London,  12mo.  1836. 

This  is  a  curious  hoax,  evidently  written  by  a  person  versed  in 
astronomy  and  clever  at  introducing  probable  circumstances  and 
undesigned  coincidences.  It  first  appeared  in  a  newspaper.  It 
makes  Sir  J.  Herschel  discover  men,  animals,  &c.  in  the  moon,  of 
which  much  detail  is  given.  There  seems  to  have  been  a  French 
edition,  the  original,  and  English  editions  in  America,  whence 
the  work  came  into  Britain :  but  whether  the  French  was  pub- 
lished in  America  or  at  Paris  I  do  not  know.  There  is  no  doubt 
that  it  was  produced  in  the  United  States,  by  M.  Nicollet,  an 
astrenomer,  once  of  Paris,  and  a  fugitive  of  some  kind.  About 


198  A  BUDGET  OF  PARADOXES. 

him  I  have  heard  two  stories.  First,  that  he  fled  to  America 
with  funds  not  his  own,  and  that  this  book  was  a  mere  device  to 
raise  the  wind.  Secondly,  that  he  was  a  protege  of  Laplace,  and 
of  the  Polignac  party,  and  also  an  outspoken  man.  That  after 
the  revolution  he  was  so  obnoxious  to  the  republican  party  that 
he  judged  it  prudent  to  quit  France;  which  he  did  in  debt, 
leaving  money  for  his  creditors,  but  not  enough,  with  M.  Bouvard. 
In  America  he  connected  himself  with  an  assurance  office.  The 
moon-story  was  written,  and  sent  to  France,  chiefly  with  the 
intention  of  entrapping  M.  Arago,  Nic'ollet's  especial  foe,  into  the 
belief  of  it.  And  those  who  narrate  this  version  of  the  story 
wind  up  by  saying  that  M.  Arago  was  entrapped,  and  circulated 
the  wonders  through  Paris,  until  a  letter  from  Nicollet  to  M. 
Bouvard  explained  the  hoax.  I  have  no  personal  knowledge  of 
either  story :  but  as  the  poor  man  had  to  endure  the  first,  it  is 
but  right  that  the  second  should  be  told  with  it. 

The  Weather  Almanac  for  the  Year  1838.     By  P.  Murphy,  Esq. 
M.N.S. 

By  M.N.S.  is  meant  member  of  no  society.  This  almanac  bears 
on  the  title-page  two  recommendations.  The  Morning  Post  calls 
it  one  of  the  most  important-if-true  publications  of  our  gene- 
ration. The  Times  says  :  *  If  the  basis  of  his  theory  prove  sound, 
and  its  principles  be  sanctioned  by  a  more  extended  experience, 
it  is  not  too  much  to  say  that  the  importance  of  the  discovery 
is  equal  to  that  of  the  longitude.'  Cautious  journalist !  Three 
times  that  of  the  longitude  would  have  been  too  little  to  .say. 
That  the  landsman  might  predict  the  weather  of  all  the  year,  at 
its  beginning,  Jack  would  cheerfully  give  up  astronomical  longi- 
tude— the  problem — altogether,  and  fall  back  on  chronometers 
with  the  older  Ls,  lead,  latitude,  and  look-out,  applied  to  dead- 
reckoning.  Mr.  Murphy  attempted  to  give  the  weather  day  by 
day :  thus  the  first  seven  days  of  March  bore  Changeable  ;  Eain  ; 
Kain  ;  Rain-wind ;  Changeable  ;  Fair  ;  Changeable.  To  aim  at 
such  precision  as  to  put  a  fair  day  between  two  changeable  ones 
by  weather  theory  was  going  very  near  the  wind  and  weather  too. 
Murphy  opened  the  year  with  cold  and  frost ;  and  the  weather 
did  the  same.  But  Murphy,  opposite  to  Saturday,  January  20, 
put  down  *  Fair,  Probable  lowest  degree  of  winter  temperature.' 
When  this  Saturday  came,  it  was  not  merely  the  probably  cold- 
est of  1838,  but  certainly  the  coldest  of  many  consecutive  years. 
Without  knowing  anything  of  Murphy,  I  felt  it  prudent  to  cover 
my  nose  with  my  glove  as  I  walked  the  street  at  eight  in  the 


MATHEMATICAL   THEOLOGY.  199 

morning.  The  fortune  of  the  Almanac  was  made.  Nobody 
waited  to  see  whether  the  future  would  dement  the  prophecy : 
the  shop  was  beset  in  a  manner  which  brought  the  police  to  keep 
order;  and  it  was  said  that  the  Almanac  for  1838  was  a  gain  of 
5,0001.  to  the  owners.  It  very  soon  appeared  that  this  was  only 
a  lucky  hit :  the  weather-prophet  had  a  modified  reputation  for  a 
few  years ;  and  is  now  no  more  heard  of.  A  work  of  his  will 
presently  appear  in  the  list. 

Letter  from  Alexandria  on  the  evidence  of  the  practical  appli- 
cation of  the  quadrature  of  the  circle  in  the  great  pyramids  of 
Gizeh.  By  H.  C.  Agnew,  Esq.  London,  1838,  4to. 

Mr.  Agnew  detects  proportions  which  he  thinks  were  suggested 
by  those  of  the  circumference  and  diameter  of  a  circle. 

The  creed  of  St.  Athanasius  proved  by  a  mathematical  parallel. 
Before  you  censure,  condemn,  or  approve  ;  read,  examine,  and- 
understand.  E.  B.  REVILO.  London,  1839,  8vo. 

This  author  really  believed  himself,  and  was  in  earnest.  He  is 
not  the  only  person  who  has  written  nonsense  by  confounding  the 
mathematical  infinite  (of  quantity)  with  what  speculators  now 
more  correctly  express  by  the  unlimited,  the  unconditioned,  or 
the  absolute.  This  tract  is  worth  preserving,  as  the  extreme  case 
of  a  particular  kind.  The  following  is  a  specimen.  Infinity 
being  represented  by  oo  ,  as  usual,  and/,  s,  g,  being  finite  integers, 
the  three  Persons  are  denoted  by  oo ',  (m  oo  )',  oo ",  the  finite 
fraction  m  representing  human  nature,  as  opposed  to  oo  .  The 
clauses  of  the  Creed  are  then  given  with  their  mathematical 
parallels.  I  extract  a  couple : — 

But  the  Godhead  of  the  Father,  It  has  been  shown  that  oo-^,  oo', 
of  the  Son,  and  of  the  Holy  Ghost,  and  (m  oo  )  *,  together,  are  but  oo  , 
is  all  one  :  the  glory  equal,  the  and  that  each  is  oo  ,  and  any  magni- 
Majesty  co-eternal.  tude  in  existence  represented  by  oo 

always  was  and  always  will  be :  for 
it  cannot  be  made,  or  destroyed,  and 
yet  exists. 

Equal  to  the  Father,  as  touching  (in  oo  )*  is  equal  to  oo^as  toucli- 
his  Godhead:  and  inferior  to  the  ing  oo  ,  but  inferior  to  oo-^as  touch- 
Father,  as  touching  his  Manhood,  ing  m  :  because  m  is  not  infinite. 

I  might  have  passed  this  over,  as  beneath  even  my  present 
subject,  but  for  the  way  in  which  I  became  acquainted  with  it. 
A  bookseller,  not  the  publisher,  handed  it  to  me  over  his  counter: 
one  who  had  published  mathematical  works.  He  said,  with  an 


200  A   BUDGET   01?'   PARADOXES. 

air  of  important  communication.  Have  you  seen  this,  Sir !    In 

reply,  I  recommended  him  to  show  it  to  my  friend  Mr. ,  for 

whom  he  had  published  mathematics.  Educated  men,  used  to 
books,  and  to  the  converse  of  learned  men,  look  with  mysterious 
wonder  on  such  productions  as  this:  for  which  reason  I  have 
made  a  quotation  which  many  will  judge  had  better  have  been 
omitted.  But  it  would  have  been  an  imposition  on  the  public  if 
I  were,  omitting  this  and  some  other  uses  of  the  Bible  and 
Common  Prayer,  to  pretend  that  I  had  given  a  true  picture  of 
my  school. 

[Since  the  publication  of  the  above,  it  has  been  stated  that  the 
author  is  Mr.  Oliver  Byrne,  the  author  of  the  Dual  Arithmetic 
mentioned  further  on :  E.  B.  Revilo  seems  to  be  obviously  a 
reversal.] 

Old  and  new  logic  contrasted  :  being  an  attempt  to  elucidate,  for 
ordinary  comprehension,  how  Lord  Bacon  delivered  the  human 
mind  from  its  2,000  years'  enslavement  under  Aristotle.  By 
Justin  Brenan.  London,  1839,  12mo. 

Logic,  though  the  other  exact  science,  has  not  had  the  sort  of 
assailants  who  have  clustered  about  Mathematics.  There  is  a 
sect  which  disputes  the  utility  of  logic,  but  there  are  no  special 
points,  like  the  quadrature  of  the  circle,  which  excite  dispute 
among  those  who  admit  other  things.  The  old  story  about 
Aristotle  having  one  logic  to  trammel  us,  and  Bacon  another  to 
set  us  free, — always  laughed  at  by  those  who  really  knew  either 
Aristotle  or  Bacon, — now  begins  to  be  understood  by  a  large 
section  of  the  educated  world.  The  author  of  this  tract  connects 
the  old  logic  with  the  indecencies  of  the  classical  writers,  and  the 
new  with  moral  purity :  he  appeals  to  women,  who,  '  when  they 
see  plainly  the  demoralizing  tendency  of  syllogistic  logic,  they 
will,  no  doubt,  exert  their  powerful  influence  against  it,  and 
support  the  Baconian  method.'  This  is  the  only  work  against 
logic  which  I  can  introduce,  but  it  is  a  rare  one,  I  mean  in 
contents.  I  quote  the  author's  idea  of  a  syllogism  : — 

The  basis  of  this  system  is  the  syllogism.  This  is  a  form  of  couch- 
ing the  substance  of  your  argument  or  investigation  into  one  short 
line  or  sentence — then  corroborating  or  supporting  it  in  another,  and 
drawing  your  conclusion  or  proof  in  a  third. 

On  this  definition  he  gives  an  example,  as  follows :  '  Every  sin 
deserves  death,'  the  substance  of  the  '  argument  or  investigation.' 
Then  comes,  '  Every  unlawful  wish  is  a  sin,'  which  '  corroborates 
or  supports  '  the  preceding  :  and,  lastly,  '  therefore  every  unlaw- 


LOGIC;   SIR  WILLIAM   HAMILTON.  201 

ful  wish  deserves  death,'  which  is  the  '  conclusion  or  proof.'  We 
learn,  also,  that  *  sometimes  the  first  is  called  the  premises  (sic), 
and  sometimes  the  first  premiss  ; '  as  also  that  l  the  first  is  some- 
times called  the  proposition,  or  subject,  or  affirmative,  and  the 
next  the  predicate,  and  sometimes  the  middle  term.'  To  which 
is  added,  with  a  mark  of  exclamation  at  the  end,  '  but,  in  analyz- 
ing the  syllogism,  there  is  a  middle  term,  and  a  predicate  too,  in 
each  of  the  lines  ! '  It  is  clear  that  Aristotle  never  enslaved  this 
mind. 

I  have  said  that  logic  has  no  paradoxers,  but  I  was  speaking  of 
old  time.  This  science  has  slept  until  our  own  day :  Hamilton 
says  there  has  been  *  no  progress  made  in  the  general  develop- 
ment of  the  syllogism  since  the  time  of  Aristotle  ;  and  in  regard 
to  the  few  partial  improvements,  the  professed  historians  seem 
altogether  ignorant.'  But  in  our  time,  the  paradoxer,  the  oppo- 
nent of  common  opinion,  has  appeared  in  this  field.  I  do  not 
refer  to  Prof.  Boole,  who  is  not  a  paradoxer,  but  a  discoverer : 
his  system  could  neither  oppose  nor  support  common  opinion, 
for  its  grounds  were  not  within  the  conception  of  any  one.  I 
speak  especially  of  two  others,  who  fought  like  cat  and  dog : 
one  was  dogmatical,  the  other  categorical.  The  first  was  Hamil- 
ton himself — Sir  William  Hamilton  of  Edinburgh,  the  meta- 
physician, not  Sir  William  Rowan  Hamilton  of  Dublin,  the 
mathematician,  a  combination  of  peculiar  genius  with  unprece- 
dented learning,  erudite  in  all  he  could  want  except  mathematics, 
for  which  he  had  no  turn,  and  in  which  he  had  not  even  a  school- 
boy's knowledge,  thanks  to  the  Oxford  of  his  younger  day.  The 
other  was  the  author  of  this  work,  so  fully  described  in  Hamil- 
ton's writings  that  there  is  no  occasion  to  describe  him  here.  I 
shall  try  to  say  a  few  words  in  common  language  about  the  para- 
doxers. 

Hamilton's  great  paradox  was  the  quantification  of  the  predi- 
cate ;  a  fearful  phrase,  easily  explained.  We  all  know  that  when 
we  say  '  Men  are  animals,'  a  form  wholly  unqualified  in  phrase, 
we  speak  of  all  men,  but  not  of  all  animals :  it  is  some  or  all, 
some  may  be  all  for  aught  the  proposition  says.  This  some-may- 
be-all-for-aught-we-say,  or  not-none,  is  the  logician's  some.  One 
would  suppose  that  '  all  men  are  some  animals,'  would  have  been 
the  logical  phrase  in  all  time :  but  the  predicate  never  was 
quantified.  The  few  who  alluded  to  the  possibility  of  such  a 
thing  found  reasons  for  not  adopting  it  over  and  above  the  great 
reason,  that  Aristotle  did  not  adopt  it.  For  Aristotle  never  ruled 
in  physics  or  metaphysics  in  the  old  time  with  near  so  much  of 


202  A  BUDGET   OF  PARADOXES. 

absolute  sway  as  he  has  ruled  in  logic  down  to  OUT  own  time. 
The  logicians  knew  that  in  the  proposition  '  all  men  are  animals  ' 
the  x  animal '  is  not  universal,  but  particular :  yet  no  one  dared 
to  say  that  all  men  are  some  animals,  and  to  invent  the  phrase, 
'  some  animals  are  all  men '  until  Hamilton  leaped  the  ditch, 
and  not  only  completed  a  system  of  enunciation,  but  applied  it  to 
syllogism. 

My  own  case  is  as  peculiar  as  his :  I  have  proposed  to  intro- 
duce mathematical  thought  into  logic  to  an  extent  which  makes 
the  old  stagers  cry 

St.  Aristotle  !  what  wild  notions  ! 
Serve  a  ne  exeat  regno  on  him ! 

Hard  upon  twenty  years  ago,  a  friend  and  opponent,  who  stands 
high  in  these  matters,  and  who  is  not  nearly  such  a  sectary  of 
Aristotle  and  establishment  as  most,  wrote  to  me  as  follows : — 
6  It  is  said  that  next  to  the  man  who  forms  the  taste  of  a  nation, 
the  greatest  genius  is  the  man  who  corrupts  it.  I  mean  therefore 
no  disrespect,  but  very  much  the  reverse,  when  I  say  that  I 
have  hitherto  always  considered  you  as  a  great  logical  heresiarch.' 
Coleridge  says  he  thinks  that  it  was  Sir  Joshua  Eeynolds  who 
made  the  remark :  which,  to  copy  a  bull  I  once  heard,  I  cannot 
deny,  because  I  was  not  there  when  he  said  it.  My  friend  did 
-  not  call  me  to  repentance  and  reconciliation  with  the  church  : 
I  think  he  had  a  guess  that  I  was  a  reprobate  sinner.  My 
offences  at  that  time  were  but  small:  I  went  on  spinning  syllo- 
gism systems,  all  alien  from  the  common  logic,  until  I  had  six, 
the  initial  letters  of  which,  put  together,  from  the  names  I  gave 
before  I  saw  what  they  would  make,  bar  all  repentance  by  the 
words 

RUE  NOT ! 

leaving  to  the  followers  of  the  old  school  the  comfortable  option 
of  placing  the  letters  thus : 

TRUE  ?  NO  ! 

It  should  however  be  stated  that  the  question  is  not  about 
absolute  truth  or  falsehood.  No  one  denies  that  anything  I  call 
an  inference  is  an  inference :  they  say  that  my  alterations  are 
extra-logical ;  that  they  are  material,  not  formal ;  and  that  logic 
is  a  formal  science. 

The  distinction  between  material  and  formal  is  easily  made, 
where  the  usual  perversions  are  not  required.  A  form  is  an 
empty  machine,  such  as  '  Every  X  is  Y ; '  it  may  be  supplied 
with  matter,  as  in  '  Every  man  is  animal.'  The  logicians  will 


LOGIC  ;  THE  HAMILTON  CONTROVERSY.  203 

foot  see  that  their  formal  proposition,  '  Every  X  is  Y,'  is  material 
in  three  points,  the  degree  of  assertion,  the  quantity  of  the 
proposition,  and  the  copula.  The  purely  formal  proposition  is 
'  There  is  the  probability  a  that  X  stands  in  the  relation  L  to 
Y.'  The  time  will  come  when  it  will  be  regretted  that  logic 
went  without  paradoxers  for  two  thousand  years :  and  when  much 
that  has  been  said  on  the  distinction  of  form  and  matter  will 
breed  jokes. 

I  give  one  instance  of  one  mood  of  each  of  the  systems,  in  the 
order  of  the  letters  first  written  above. 

Relative. — In  this  system  the  formal  relation  is  taken,  that  is, 
the  copula  may  be  any  whatever.  As  a  material  instance,  in 
which  the  relations  are  those  of  consanguinity  (of  men  under- 
stood), take  the  following:  X  is  the  brother  of  Y ;  X  is  not  the 
uncle  of  Z  ;  therefore,  Z  is  not  the  child  of  Y.  The  discussion  of 
relation,  and  of  the  objections  to  the  extension,  is  in  the  Cam- 
bridge Transactions,  vol.  x,  part  2  ;  a  crabbed  conglomerate. 

Undecided. — In  this  system  one  premise,  and  want  of  power 
over  another,  infer  want  of  power  over  a  conclusion.  As  '  Some 
men  are  not  capable  of  tracing  consequences ;  we  cannot  be  sure 
that  there  are  beings  responsible  for  consequences  who  are  in- 
capable of  tracing  consequences  ;  therefore,  we  cannot  be  sure 
that  all  men  are  responsible  for  the  consequences  of  their  ac- 
tions.' 

Exemplar. — This,  long  after  it  suggested  itself  to  me  as  a 
means  of  correcting  a  defect  in  Hamilton's  system,  I  saw  to  be 
the  very  system  of  Aristotle  himself,  though  his  followers  have 
drifted  into  another.  It  makes  its  subject  and  predicate  ex- 
amples, thus :  Any  one  man  is  an  animal ;  any  one  animal  is  a 
mortal ;  therefore,  any  one  man  is  a  mortal. 

Numerical. — Suppose  100  Ys  to  exist:  then  if  70  Xs  be  Ys, 
and  40  Zs  be  Ys,  it  follows  that  10  Xs  (at  least)  are  Zs.  Hamil- 
ton, whose  mind  could  not  generalize  on  symbols,  saw  that  the 
word  most  would  come  under  this  system,  and  admitted,  as  valid, 
such  a  syllogism  as  '  mpst  Ys  are  Xs  ;  most  Ys  are  Zs ;  therefore, 
some  Xs  are  Zs.' 

Onymatic. — This  is  the  ordinary  system  much  enlarged  in 
prepositional  forms.  It  is  fully  discussed  in  my  Syllabus  of 
Logic. 

Transposed. — In  this  syllogism  the  quantity  in  one  premise  is 
transposed  into  the  other.  As,  some  Xs  are  not  Ys ;  for  every  X 
there  is  a  Y  which  is  Z ;  therefore,  some  Zs  are  not  Xs. 

Sir   William  Hamilton   of  Edinburgh   was   one    of  the  best 


204  A  BUDGET   OP  PAKADOXES. 

friends  and  allies  I  ever  had.  When  I  first  began  to  publish 
speculation  on  this  subject,  he  introduced  me  to  the  logical 
world  as  having  plagiarized  from  him.  This  drew  their  attention  : 
a  mathematician  might  have  written  about  logic  under  forms 
which  had  something  of  mathematical  look  long  enough  before  the 
Aristotelians  would  have  troubled  themselves  with  him :  as  was 
done  by  John  Bernoulli,  James  Bernoulli,  Lambert,  and  Grergonne  ; 
who,  when  our  discussion  began,  were  not  known  even  to  omnile- 
gent  Hamilton.  He  retracted  his  accusation  of  wilful  theft  in 
a  manly  way  when  he  found  it  untenable  ;  but  on  this  point  he 
wavered  a  little,  and  was  convinced  to  the  last  that  I  had  taken 
his  principle  unconsciously.  He  thought  I  had  done  the  same 
with  Ploucquet  and  Lambert.  It  was  his  pet  notion  that  I  did 
not  understand  the  commonest  principles  of  logic,  that  I  did  not 
always  know  the  difference  between  the  middle  term  of  a  syllo- 
gism and  its  conclusion.  It  went  against  his  grain  to  imagine 
that  a  mathematician  could  be  a  logician.  So  long  as  he 
took  me  to  be  riding  my  own  hobby,  he  laughed  consumedly : 
but  when  he  thought  he  could  make  out  that  I  was  mounted 
behind  Ploucquet  or  Lambert,  the  current  ran  thus : — '  It  would 
indeed  have  been  little  short  of  a  miracle  had  he,  ignorant  even 
of  the  common  principles  of  logic,  been  able  of  himself  to  rise  to 
generalization  so  lofty  and  so  accurate  as  are  supposed  in  the 
peculiar  doctrines  of  both  the  rival  logicians,  Lambert  and 
Ploucquet — how  useless  soever  these  may  in  practice  prove  to  be. 
All  this  has  been  sufficiently  discussed  elsewhere  :  '  but,  masters, 
remember  that  I  am  an  ass.' 

I  know  that  I  never  saw  Lambert's  work  until  after  all 
Hamilton  supposed  me  to  have  taken  was  written :  he  himself, 
who  read  almost  everything,  knew  nothing  about  it  until  after  I 
did.  I  cannot  prove  what  I  say  about  my  knowledge  of  Lambert : 
but  the  means  of  doing  it  may  turn  up.  For,  by  the  casual 
turning  up  of  an  old  letter,  I  have  found  the  means  of  clearing 
myself  as  to  Ploucquet.  Hamilton  assumed  that  (unconsciously) 
I  took  from  Ploucquet  the  notion  of  a  logical  notation  in  which 
the  symbol  of  the  conclusion  is  seen  in  the  joint  symbols  of  the 
premises.  For  example,  in  my  own  fashion  I  write  down  (•)(•)' 
two  symbols  of  premises.  By  these  symbols  I  see  that  there  is  a 
valid  conclusion,  and  that  it  may  be  written  in  symbol  by  striking 
out  the  two  middle  parentheses,  which  gives  (  .  .  )  and  reading 
the  two  negative  dots  as  an  affirmative.  And  so  I  see  in  (.)(.) 
that  (  )  is  the  conclusion.  This,  in  full,  is  the  perception  that 
*  all  are  either  Xs  or  Ys '  and  '  all  are  either  Ys  or  Zs '  necessitates 
'gome  Xs  are  Zs.'  Now  in  Ploucquet's  book  of  1763,  is  found, 


CONTROVERSY  WITH  HAMILTON.  205 

1  Deleatur  in  praemissis  medius ;  id  quod  restat  indicat  con- 
clusionem.'  In  the  paper  in  which  I  explain  my  symbols — which 
are  altogether  different  from  Ploucquet's — there  is  found  '  Erase 
the  symbols  of  the  middle  term  ;  the  remaining  symbols  show 
the  inference.'  There  is  very  great  likeness :  and  I  would  have 
excused  Hamilton  for  his  notion  if  he  had  fairly  given  reference  to 
the  part  of  the  book  in  which  his  quotation  was  found.  For  I 
had  shown  in  my  Formal  Logic  what  part  of  Ploucquet's  book  I 
had  used :  and  a  fair  disputant  would  either  have  strengthened 
his  point  by  showing  that  I  had  been  at  his  part  of  the  book,  or 
allowed  me  the  advantage  of  it  being  apparent  that  I  had  not 
given  evidence  of  having  seen  that  part  of  the  book.  My  good 
friend,  though  an  honest  man,  was  sometimes  unwilling  to  allow 
due  advantage  to  controversial  opponents. 

But  to  my  point.  The  only  work  of  Ploucquet  I  ever  saw  was 
lent  me  by  my  friend  Dr.  Logan,  with  whom  I  have  often  corres- 
ponded on  logic,  &c.  I  chanced  (in  1865)  to  turn  up  the  letter 
which  he  sent  me  (Sept.  12,  1847)  with  the  book.  Part  of  it 
runs  thus : — '  I  congratulate  you  on  your  success  in  your  logical 
researches  [that  is,  in. asking  for  the  book,  I  had  described  some 
results].  Since  the  reading  of  your  first  paper  I  have  been 
satisfied  as  to  the  possibility  of  inventing  a  logical  notation  in 
which  the  rationale  of  the  inference  is  contained  in  the  symbol, 
though  I  never  attempted  to  verify  it  [what.  I  communicated, 
then,  satisfied  the  writer  that  I  had  done  and  communicated  what 
he,  from  my  previous  paper,  suspected  to  be  practicable],  I 
send  you  Ploucquet's  dissertation.  .  .  .' 

It  now  being  manifest  that  I  cannot  be  souring  grapes  which 
have  been  taken  from  me,  I  will  say  what  I  never  said  in  print 
before.  There  is  not  the  slightest  merit  in  making  the  symbols 
of  the  premises  yield  that  of  the  conclusion  by  erasure  :  the  thing 
must  do  itself  in  every  system  which  symbolises  quantities.  For 
in  every  syllogism  (except  the  inverted  Bramantip  of  the  Aristo- 
telians) the  conclusion  is  manifest  in  this  way  without  symbols. 
This  Bramantip  destroys  system  in  the  Aristotelian  lot:  and 
circumstances  which  I  have  pointed  out  destroy  it  in  Hamilton's 
own  collection.  But  in  that  enlargement  of  the  reputed  Aristo- 
telian system  which  I  have  called  onymatic,  and  in  that  correction 
of  Hamilton's  system  which  I  have  called  exemplar,  the  rule  of 
erasure  is  universal,  and  may  be  seen  without  symbols. 

Our  first  controversy  was  in  1846.  In  1847,  in  my  Formal 
Logic,  I  gave  him  back  a  little  satire  for  satire,  just  to  show,  as 
1  stated,  that  I  could  employ  ridicule  if  I  pleased.  He  was  so 


206  A  BUDGET  OF  PARADOXES. 

offended  with  the  appendix  in  which  this  was  contained,  that  he 
would  not  accept  the  copy  of  the  book  I  sent  him,  but  returned 
it.  Copies  of  controversial  works,  sent  from  opponent  to  opponent, 
are  not  presents,  in  the  usual  sense :  it  was  a  marked  success  to 
make  him  angry  enough  to  forget  this.  It  had  some  effect  how- 
ever :  during  the  rest  of  his  life  I  wished  to  avoid  provocation  ;  for 
I  could  not  feel  sure  that  excitement  might  not  produce  con- 
sequences. I  allowed  his  slashing  account  of  me  in  the  Discus- 
sions to  pass  unanswered  :  and  before  that,  when  he  proposed  to 
open  a  controversy  in  the  Athenaeum  upon  my  second  Cambridge 
paper,  I  merely  deferred  the  dispute  until  the  next  edition  of  my 
Formal  Logic.  I  cannot  expect  the  account  in  the  Discussions 
to  amuse  an  unconcerned  reader  as  much  as  it  amused  myself : 
but  for  a  cut-and-thrust,  might-and-main,  tooth-and-nail,  ham- 
mer-and-tongs  assault,  I  can  particularly  recommend  it.  I  never 
knew,  until  I  read  it,  how  much  I  should  enjoy  a  thundering 
onslaught  on  myself,  done  with  racy  insolence  by  a  master  hand, 
to  whom  my  good  genius  had  whispered  Ita  feri  ut  se  sentiat 
emori.  Since  that  time  I  have,  as  the  Irishman  said,  become  '  dry 
moulded  for  want  of  a  bating.'  Some  of  my  paradoxers  have 
done  their  best :  but  theirs  is  mere  twopenny — '  small  swipes,'  as 
Peter  Peebles  said.  Brandy  for  heroes !  I  hope  a  reviewer  or  two 
will  have  mercy  on  me,  and  will  give  me  as  good  discipline  as 
Strafford  would  have  given  to  Hampden  and  his  set:  'much 
beholden,'  said  he,  '  should  they  be  to  any  one  that  should 
thoroughly  take  pains  with  them  in  that  kind  ' — meaning  objective 
flagellation.  And  I  shall  be  the  same  to  any  one  who  will  serve 
me  so — but  in  a  literary  and  periodical  sense :  my  corporeal 
cuticle  is  as  thin  as  my  neighbours'. 

Sir  W.  H.  was  suffering  under  local  paralysis  before  our  con- 
troversy commenced  :  and  though  his  mind  was  quite  unaffected, 
a  retort  of  as  downright  a  character  as  the  attack  might  have 
produced  serious  effect  upon  a  person  who  had  shown  himself 
sensible  of  ridicule.  Had  a  second  attack  of  his  disorder  followed 
an  answer  from  me,  I  should  have  been  held  to  have  caused  it : 
though,  looking  at  Hamilton's  genial  love  of  combat,  I  strongly 
suspected  that  a  retort  in  kind 

Would  cheer  his  heart,  and  warm  his  blood, 
And  make  him  fight,  and  do  him  good. 

But  I  could  not  venture  to  risk  it.  So  all  I  did,  in  reply  to  the 
article  in  the  Discussions,  was  to  write  to  him  the  following  note  : 
which,  as  illustrating  an  etiquette  of  controversy,  I  insert. 


LETTER   TO   HAMILTON— DOGGR EL.  207 

'  I  beg  to  acknowledge  and  thank  you  for  .  .  .  It  is  necessary  that  I 
should  say  a  word  on  my  retention  of  this  work,  with  reference  to 
your  return  of  the  copy  of  my  '  Formal  Logic,'  which  I  presented  to 
you  on  its  publication  :  a  return  made  on  the  ground  of  your  disap- 
proval of  the  account  of  our  controversy  which  that  work  contained. 
According  to  my  view  of  the  subject,  any  one  whose  dealing  with  the 
author  of  a  book  is  specially  attacked  in  it,  has  a  right  to  expect  from 
the  author  that  part  of  the  book  in  which  the  attack  is  made,  together 
with  so  much  of  the  remaining  part  as  is  fairly  context.  And  I  hold 
that  the  acceptance  by  the  party  assailed  of  such  work  or  part  of  a  work 
does  not  imply  any  amount  of  approval  of  the  contents,  or  of  want  of 
disapproval.  On  this  principle  (though  I  am  not  prepared  to  add  the 
word  alone)  I  forwarded  to  you  the  whole  of  my  work  on  "  Formal 
Logic  "  and  my  second  Cambridge  Memoir.  And  on  this  principle  I 
should  have  held  you  wanting  in  due  regard  to  my  literary  rights  if 
you  had  not  forwarded  to  me  your  asterisked  pages,  with  all  else  that 
was  necessary  to  a  full  understanding  of  their  scope  and  meaning,  so 
far  as  the  contents  of  the  book  would  furnish  it.  For  the  remaining 
portion,  which  it  would  be  a  hundred  pities  to  separate  from  the  pag^es 
in  which  I  am  directly  concerned,  I  am  your  debtor  on  another  princi- 
ple ;  and  shall  be  glad  to  remain  so  if  you  will  allow  me  to  make  a 
feint  of  balancing  the  account  by  the  offer  of  two  small  works  on  sub- 
jects as  little  connected  with  our  discussion  as  the  "  Epistolae  Obscuro- 
rum  Yirorum,"  or  the  Lutheran  dispute.  I  trust  that  by  accepting 
my  "  Opuscula  "  you  will  enable  me  to  avoid  the  use  of  the  knife,  and 
leave  me  to  cut  you  up  with  the  pen  as  occasion  shall  serve,  I  remain, 
&c.  (April  21,  1852).' 

I  received  polite  thanks,  but  not  a  word  about  the  body  of  the 
letter :  my  argument,  I  suppose,  was  admitted. 

I  find  among  my  miscellaneous  papers  the  following  jeu 
desprit,  or  jeu  de  betise,  whichever  the  reader  pleases — I  care 
not  — intended,  before  I  saw  ground  for  abstaining,  to  have,  as  the 
phrase  is,  come  in  somehow.  I  think  I  could  manage  to  bring 
anything  into  anything :  certainly  into  a  Budget  of  Paradoxes. 
Sir  W.  H.  rather  piqued  himself  upon  some  caniculars,  or  doggrel 
verses,  which  he  had  put  together  in  memoriam  [technicam]  of 
the  way  in'  which  A  E  I  0  are  used  in  logic  :  he  added  U,  Y,  for 
the  addition  of  meet,  &c.  to  the  system.  I  took  the  liberty  of 
concocting  some  counter-doggrel,  just  to  show  that  a  mathema- 
tician may  have  architectonic  power  as  well  as  a  metaphysician. 


208  A  BUDGET   OF  PAEADOXES. 

DOGGREL. 
BY  SIR  W.  HAMILTON. 

A  it  affirms  of  this,  these,  all, 

Whilst  E  deries  of  any  • 
I  it  affirms  (whilst  O  denies) 

Of  some  (or  few,  or  many). 

Thus  A  affirms,  as  E  denies, 

And  definitely  either ; 
Thus  I  affirms,  as  0  denies, 

And  definitely  neither. 

A  half,  left  semidefinite, 

Is  worthy  of  its  score  ; 
TJ,  then,  affirms,  as  Y  denies, 

This,  neither  less  nor  more. 

Indefinito-definites, 

I,  UI,  YO,  last  we  come ; 
And  this  affirms,  as  that  denies 

Of  more,  most  (half,  plus,  some). 

COUNTER  DOGGREL. 

BY  PROF.  DE  MORGAN. 
(1847.) 

GREAT  A  affirms  of  all ; 

SJr  William  does  so  too  : 
When  the  subject  is  '  my  suspicion,' 

And  the  predicate  '  must  be  true.' 

Great  E  denies  of  all ; 

Sir  William  of  all  but  one  : 
When  he  speaks  about  this  present  time, 

And  of  those  who  in  logic  have  done. 

Great  I  takes  up  but  some  ; 

Sir  William  !  my  dear  soul ! 
Why  then  in  all  your  writings, 

Does  '  Great  I '  fill1  the  whole  ! 

1  A  very  truculently  unjust  assertion  :  for  Sir  W.  was  as  great  a  setter  up  of  some 
as  lie  was  a  puller  down  of  others.  His  writings  are  a  congeries  of  praises  and 
blames,  both  cruel  smart,  as  they  say  in  the  States.  But  the  combined  instigation  of 


LOGICAL  DOGGREL.  209 

Great  O  says  some  are  not ; 

Sir  William's  readers  catch, 
That  some  (modern)  Athens  is  not  without 

An  Aristotle  to  match, 

*  A  half,  left  semi-definite, 

Is  worthy  of  its  score : ' 
This  looked  very  much  like  balderdash, 

And  neither  less  nor  more. 

It  puzzled  me  like  anything  ; 

In  fact,  it  puzzled  me  worse  : 
Isn't  schoolman's  logic  hard  enough, 

Without  being  in  Sibyl's  verse  ? 

At  last,  thinks  I,  'tis  German  ; 

And  I'll  try  it  with  some  beer ! 
The  landlord  asked  what  bothered  me  so, 

And  at  once  he  made  it  clear. 

It's  half-and-half,  the  gentleman  means ; 

Don't  you  see  he  talks  of  score  ? 
That's  the  bit  of  a  memorandum 

That  we  chalk  behind  .the  door. 

Semi-definite  's  outlandish ; 

But  I  see,  in.  half  a  squint, 
That  he  speaks  of  the  lubbers  who  call  for  a  quart, 

When  they  can't  manage  more  than  a  pint. 

Now  I'll  read  it  into  English, 

And  then  you'll  answer  me  this  : 
If  it  isn't  good  logic  all  the  world  round, 

I  should  like  to  know  what  is  ? 

When  you  call  for  a  pot  of  half-and-half, 

If  you're  lost  to  sense  of  shame, 
You  may  leave  it  semi-definite, 

But  you  pay  for  it  all  just  the  same. 


I  am  unspeakably  comforted  when  I  look  over  the  above  in 
remembering  that  the  question  is  not  whether  it  be  Pindaric  or 

prose,  rhyme,  and  retort  would  send  Aristides  himself  to  Tartarus,  if  it  were  not 
pretty  certain  that  Minos  would  grant  a  stet  proccssits  under  the  circumstances.  The 
first  two  verses  are  exaggerations  standing  on  a  basis  of  truth.  The  fourth  verse  is 
quite  true :  Sir  W.  H.  was  an  Edinburgh  Aristotle,  with  the  differences  of  ancient  and 
modern  Athens  well  marked,  especially  the  perfervidum  inginium  Scot&rum. 

P 


210  A   BUDGET  OF  PARADOXES. 

Horatian,  but  whether  the  copy  be  as  good  as  the  original.  And 
I  say  it  is  :  and  will  take  no  denial. 

Long  live — long  will  live — the  glad  memory  of  William 
Hamilton,  Good,  Learned,  Acute,  and  Disputatious !  He  fought 
upon  principle  :  the  motto  of  his  book  is — 

Truth,  like  a  torch,  the  more  it's  shook  it  shines. 

There  is  something  in  this ;  but  metaphors,  like  puddings, 
quarrels,  rivers,  and  arguments,  always  have  two  sides  to  them. 
For  instance, 

Truth,  like  a  torch,  the  more  ifc  's  shook  it  shines ; 

But  those  who  want  to  use  it,  hold  it  steady. 
They  shake  the  flame  who  like  a  glare  to  gaze  at, 

They  keep  it  still  who  want  a  light  to  see  by. 


Theory  of  Parallels.  The  proof  of  Euclid's  axiom  looked  for  in 
the  properties  of  the  Equiangular  Spiral.  By  Lieut-Col.  G.  Per- 
ronet  Thompson.  The  same,  second  edition,  revised  and  cor- 
rected. The  same,  third  edition,  shortened,  and  freed  from 
dependence  on  the  theory  of  limits.  The  same,  fourth  edition, 
ditto,  ditto.  All  London,  1840,  8vo. 

To  explain  these  editions  it  should  be  noted  that  General 
Thompson  rapidly  modified  his  notions,  and  republished  his  tracts 
accordingly. 

Vestiges  of  the  Natural  History  of  Creation.     London,  1840, 12mo. 

This  is  the  first  edition  of  this  celebrated  work.  Its  form  is  a 
case  of  the  theory :  the  book  is  an  undeniable  duodecimo,  but  the 
size  of  its  paper  gives  it  the  look  of  not  the  smallest  of  octavos. 
Does  not  this  illustrate  the  law  of  development,  the  gradation  of 
families,  the  transference  of  species,  and  so  on  ?  If  so,  I  claim 
the  discovery  of  this  esoteric  testimony  of  the  book  to  its  own 
contents ;  I  defy  any  one  to  point  out  the  reviewer  who  has 
mentioned  it.  The  work  itself  is  described  by  its  author  aa  '  the 
first  attempt  to  connect  the  natural  sciences  into  a  history  of 
creation.'  The  attempt  was  commenced,  and  has  been  carried 
on,  both  with  marked  talent,  and  will  be  continued.  Great 
advantage  will  result :  at  the  worst  we  are  but  in  the  alchemy  of 
some  new  chemistry,  or  the  astrology  of  some  new  astronomy. 
Perhaps  it  would  be  as  well  not  to  be  too  sure  on  the  matter, 
until  we  have  an  antidote  to  possible  consequences  as  ex- 


THE  VESTIGES   OF  CREATION.  211 

hibited  under  another  theory,  on  which  it  is  as  reasonable  to 
speculate  as  on  that  of  the  '  Vestiges.'  I  met  long  ago  with  a 
splendid  player  on  the  guitar,  who  assured  me,  and  was  confirmed 
by  his  friends,  that  he  never  practised,  except  in  thought,  and 
did  not  possess  an  instrument :  he  kept  his  fingers  acting  in  his 
mind,  until  they  got  their  habits ;  and  thus  he  learnt  the  most 
difficult  novelties  of  execution.  Now  what  if  this  should  be  a 
minor  segment  of  a  higher  law  ?  What  if,  by  constantly  think- 
ing of  ourselves  as  descended  from  primaeval  monkeys,  we  should, 
— if  this  be  true — actually  get  our  tails  again?  What  if  the 
first  man  who  was  detected  with  such  an  appendage  should  be 
obliged  to  confess  himself  the  author  of  the  '  Vestiges  ' — a  person 
yet  unknown — who  would  naturally  get  the  start  of  his  species 
by  having  had  the  earliest  habit  of  thinking  on  the  mattei  ?  I 
confess  I  never  hear  a  man  of  note  talk  fluently  about  it  without  a 
curious  glance  at  his  proportions,  to  see  whether  there  may  be 
ground  to  conjecture  that  he  may  have  more  of  '  mortal  coil ' 
than  others,  in  anaxyridical  concealment.  I  do  not  feel  sure 
that  even  a  paternal  love  for  his  theory  would  induce  him,  in  the 
case  I  am  supposing,  to  exhibit  himself  at  the  British  Associa- 
tion, 

With  a  hole  behind  which  his  tail  peeped  through. 

The  first  sentence  of  this  book  (1840)  is  a  cast  of  the  log,  which 
shows  our  rate  of  progress.  '  It  is  familiar  knowledge  that  the 
earth  which  we  inhabit  is  a  globe  of  somewhat  less  than  8,000 
miles  in  diameter,  being  one  of  a  series  of  eleven  which  revolve  at 
different  distances  around  the  sun.'  The  eleven !  Not  to  mention 
the  Iscariot  which  Le  Verrier  and  Adams  calculated  into  existence, 
there  is  more  than  a  septuagint  of  new  planetoids. 

The  Constitution  and  Rules  of  the  Ancient  and  Universal  '  Benefit 
Society '  established  by  Jesus  Christ,  exhibited,  and  its  advan- 
tages and  claims  maintained,  against  all  Modern  and  merely 
Human  Institutions  of  the  kind  :  A  Letter  very  respectfully  ad- 
dressed to  the  Rev.  James  Everett,  and  occasioned  by  certain 
remarks  made  by  him,  in  a  speech  to  the  Members  of  the 
*  Wesleyan  Centenary  Institute '  Benefit  Society.  Dated  York, 
Dec.  7,  1840.  By  Thomas  Smith.  12mo.  (pp.  8.) 

The  Wesleyan  minister  addressed  had  advocated  provision 
against  old  age,  &c. :  the  writer  declares  all  private  provision 
unchristian.  After  decent  maintenance  and  relief  of  family 
claims  of  indigence,  he  holds  that  all  the  rest  is  to  go  to  the 
'  Benefit  Society,'  of  which  he  draws  up  the  rules,  in  technical 

F   2 


212  A  BUDGET   OF  PARADOXES. 

form,  with  chapters  of  '  Officers,'  *  Contributors,'  &c.,  from  the 
Acts  of  the  Apostles,  &c.,  and  some  of  the  early  Fathers.  He 
holds  that  a  Christian  may  not  '  make  a  private  provision  against 
the  contingencies  of  the  future : '  and  that  the  great  '  Benefit 
Society '  is  the  divinely-ordained  recipient  of  all  the  surplus  of 
his  income ;  capital,  beyond  what  is  necessary  for  business,  he 
is  to  have  none.  A  real  good  speculator  shuts  his  eyes  by 
instinct,  when  opening  them  would  not  serve  the  purpose:  he 
has  the  vizor  of  the  Irish  fairy  tale,  which  fell  of  itself  over  the 
eyes  of  the  wearer  the  moment  he  turned  them  upon  the  en- 
chanted light  which  would  have  destroyed  him  if  he  had  caught 
sight  of  it.  'Whiles  it  remained,  was  it  not  thine  own?  and 
after  it  was  sold,  was  it  (the  purchase-money)  not  in  thine  own 
power?'  would  have  been  awkward  to  quote,  and  accordingly 
nothing  is  stated  except  the  well-known  result,  which  is  rule  3, 
cap.  5,  '  Prevention  of  Abuses.'  By  putting  his  principles  to- 
gether, the  author  can  be  made,  logically,  to  mean  that  the 
successors  of  the  apostles  should  put  to  death  all  contributors  who 
are  detected  in  not  paying  their  full  premiums. 

I  have  known  one  or  two  cases  in  which  policy-holders  have 
surrendered  their  policies  through  having  arrived  at  a  conviction 
that  direct  provision  is  unlawful.  So  far  as  I  could  make  it  out, 
these  parties  did  not  think  it  unlawful  to  lay  by  out  of  income, 
except  when  this  was  done  in  a  manner  which  involved  calcula- 
tion of  death-chances.  It  is  singular  they  did  not  see  that  the 
entrance  of  chance  of  death  was  the  entrance  of  the  very  principle 
of  the  benefit  society  described  in  the  Acts  of  the  Apostles.  The 
family  of  the  one  who  died  young  received  more  in  proportion  to 
premiums  paid  than  the  family  of  the  one  who  died  old.  Every 
one  who  understands  life  assurance  sees  that — bonus  apart — the 
difference  between  an  assurance  office  and  a  savings  bank  consists 
in  the  adoption,  pro  tanto,  of  the  principle  of  community  of 
goods.  In  the  original  constitution  of  the  oldest  assurance  office, 
the  Amicable  Society,  the  plan  with  which  they  started  was 
nothing  but  this :  persons  of  all  ages  under  forty-five  paid  one 
common  premium,  and  the  proceeds  were  divided  among  the 
representatives  of  those  who  died  within  the  year. 

[I  omitted  from  its  proper  place  a  manuscript  quadrature 
(3' 14 16  exactly)  addressed  to  an  eminent  mathematician,  dated 
in  1842  from  the  debtors'  ward  of  a  country  gaol.  The  unfortu- 
nate speculator  says,  '  I  have  laboured  many  years  to  find  the 
precise  ratio.'  I  have  heard  of  several  cases  in  which  squaring 


PEEPETUAL   MOTION — GEAVITATION   AND   MAGNETISM.      £13 

the  circle  has  produced  an  inability  to  square  accounts.  I  re- 
mind those  who  feel  a  kind  of  inspiration  to  employ  native 
genius  upon  difficulties,  without  gradual  progression  from  ele- 
ments, that  the  call  is  one  which  becomes  stronger  and  stronger, 
and  may  lead,  as  it  has  led,  to  abandonment  of  the  duties  of  life, 
and  all  the  consequences.] 

1842.  Provisional  Prospectus  of  the  Double  Acting  Rotary  Engine 
Company.  Also  Mechanic's  Magazine,  March  26,  1842. 

Perpetual  motion  by  a  drum  with  one  vertical  half  in  mercury, 
the  other  in  a  vacuum :  the  drum,  I  suppose,  working  round  for 
ever  to  find  an  easy  position.  Steam  to  be  superseded :  steam 
and  electricity  convulsions  of  nature  never  intended  by  Provi- 
dence for  the  use  of  man.  The  price  of  the  present  engines, 
as  old  iron,  will  buy  new  engines  that  will  work  without  fuel 
and  at  no  expense.  Guaranteed  by  the  Count  de  Predaval,  the 
discoverer.  I  was  to  have  been  a  Director,  but  my  name  got  no 
further  than  ink,  and  not  so  far  as  official  notification  of  the 
honour,  partly  owing  to  my  having  communicated  to  the 
Mechanic's  Magazine  information  privately  given  to  me,  which 
gave  premature  publicity,  and  knocked  up  the  plan. 

An  Exposition  of  the  Nature,  Force,  Action,  and  other  properties 
of  Gravitation  on  the  Planets.  London,  1842,  12mo. 

An  Investigation  of  the  principles  of  the  Rules  for  determining  the 
Measures  of  the  Areas  and  Circumferences  of  Circular  Plane 
Surfaces  .  .  .  London,  1844,  8vo. 

These  are  anonymous ;  but  the  author  (whom  I  believe  to  be 
Mr.  Denison,  presently  noted)  is  described  as  author  of  a  new 
system  of  mathematics,  and  also  of  mechanics.  He  had  need 
have  both,  for  he  shows  that  the  line  which  has  a  square  equal 
to  a  given  circle,  has  a  cube  equal  to  the  sphere  on  the  same 
diameter :  that  is,  in  old  mathematics,  the  diameter  is  to  the 
circumference  as  9  to  161  Again,  admitting  that  the  velocities 
of  planets  in  circular  orbits  are  inversely  as  the  square  roots  of 
their  distances,  that  is,  admitting  Kepler's  law,  he  manages  to 
prove  that  gravitation  is  inversely  as  the  square  root  of  the 
distance :  and  suspects  magnetism  of  doing  the  difference  be- 
tween this  and  Newton's  law.  Magnetism  and  electricity  are,  in 
physics,  the  member  of  parliament  and  the  cabman — at  every 
man's  bidding,  as  Henry  Warburton  said. 


214  A  BUDGET   OF  PARADOXES. 

The  above  is  an  outrageous  quadrature.  In  the  preceding  year, 
1841,  was  published  what  I  suppose  at  first  to  be  a  Maori  quadra- 
ture, by  Maccook.  But  I  get  it  from  a  cutting  out  of  some 
French  periodical,  and  I  incline  to  think  that  it  must  be  by  a 
Mr.  M'Cook.  He  maks  TT  to  be  2  +  2  V(8  V  2  - 1 1). 


Refutation  of  a  Pamphlet  written  by  the  Rev.  John  Mackey, 
R.C.P.,  entitled  '  A  method  of  making  a  cube  double  of  a  cube, 
founded  on  the  principles  of  elementary  geometry,'  wherein  his 
principles  are  proved  erroneous,  and  the  required  solution  not 
yet  obtained.  By  Robert  Murphy.  Mallow,  1824,  12mo. 

This  refutation  was  the  production  of  an  Irish  boy  of  eighteen 
years  old,  self-educated  in  mathematics,  the  son  of  a  shoemaker 
at  Mallow.  He  died  in  1843,  leaving  a  name  which  is  well 
known  among  mathematicians.  His  works  on  the  theory  of 
equations  and  on  electricity,  and  his  papers  in  the  Cambridge 
Transactions,  are  all  of  high  genius.  The  only  account  of  him 
which  I  know  of  is  that  which  I  wrote  for  the  Supplement  of  the 
Penny  Cyclopaedia.  He  was  thrown  by  his  talents  into  a  good 
income  at  Cambridge,  with  no  social  training  except  penury,  and 
very  little  intellectual  training  except  mathematics.  He  fell 
into  dissipation,  and  his  scientific  career  was  almost  arrested  : 
but  he  had  great  good  in  him,  to  my  knowledge.  A  sentence  in 
a  letter  from  the  late  Bean  Peacock  to  me — giving  some  advice 
about  the  means  of  serving  Murphy — sets  out  the  old  case : 
*  Murphy  is  a  man  whose  special  education  is  in  advance  of  his 
general',  and  such  men  are  almost  always  difficult  subjects  to 
manage.'  This  article  having  been  omitted  in  its  proper  place, 
I  put  it  at  1843,  the  date  of  Murphy's  death. 


The  Invisible  Universe  disclosed ;  or,  the  real  Plan  and  Govern- 
ment of  the  Universe.  By  Henry  Coleman  Johnson,  Esq. 
London,  1843,  8vo. 

The  book  opens  abruptly  with — 

"  First  demonstration.  Concerning  the  centre :  showing  that,  be- 
cause the  centre  is  an  innermost  point  at  an  equal  distance  between 
two  extreme  points  of  a  right  line,  and  from  every  two  relative  and 
opposite  intermediate  points,  it  is  composed  of  the  two  extreme  in- 
ternal points  of  each  half  of  the  line ;  each  extreme  internal  point 
attracting  towards  itself  all  parts  of  that  half  to  which  it  belongs  .  .  ." 


THE   COMET   OF    1843.  215 

Of  course  the  circle  is  squared:  and  the  circumference  is  3^ 
diameters. 

Combination  of  the  Zodiacal  and  Cometical  Systems.     Printed  for 
the  London  Society,  Exeter  Hall.     Price  Sixpence,   (n.d.  1843.) 

What  this  London  Society  was,  or  the  '  combination,'  did  not 
appear.  There  was  a  remarkable  comet  in  1843,  the  tail  of 
which  was  at  first  confounded  with  what  is  called  the  zodiacal 
light.  This  nicely-printed  little  tract,  evidently  got  up  with 
less  care  for  expense  than  is  usual  in  such  works,  brings  together 
all  the  announcements  of  the  astronomers,  and  adds  a  short  head 
and  tail  piece,  which  I  shall  quote  entire.  As  the  announce- 
ments are  very  ordinary  astronomy,  the  reader  will  be  able  to 
detect,  if  detection  be  possible,  what  is  the  meaning  and 
force  of  the  '  Combination  of  the  Zodiacal  and  Cometical  Sys- 
tems ' : — 

"  Premonition.  It  h^s  pleased  the  AUTHOR  OF  CREATION  to  cause  (to 
His  human  and  reasoning  Creatures  of  this  generation,  by  a  '  combined ' 
appearance  in  His  Zodiacal  and  Cometical  systems)  a  '  warning  Crisis  ' 
of  universal  concernment  to  this  our  GLOBE.  It  is  this  '  Crisis '  that 
has  so  generally  '  ROUSED  '  at  this  moment  the  '  nations  throughout  the 
Earth '  that  no  equal  interest  has  ever  before  been  excited  by  MAN  ; 
unless  it  be  in  that  caused  by  the  '  PAGAN- TEMPLE  IN  ROME,' which 
is  recorded  by  the  elder  Pliny,  l  Nat.  Hist.'  i.  23.  iii.  3.  HARDOUIN." 

After  the  accounts  given  by  the  unperceiving  astronomers,  comes 
what  follows : — 

"  Such  has  been  (hitherto)  the  only  object  discerned  by  the  '  Wise  of 
this  World,'  in  this  twofold  union  of  the  '  Zodiacal '  and  '  Cometical ' 
systems :  yet  it  is  nevertheless  a  mcst  '  Thrilling  Warning,'  to  all  the 
inhabitants  of  this  precarious  and  transitory  EARTH.  We  have  no 
authorized  intimation,  or  reasonable  prospective  contemplation,  of 

*  current  time  '  beyond  a  year  1860,  of  the  present  century  ;  or  rather, 
except  '  the  interval  which  may  now  remain  from  the  present  year  3843, 
to  a  year  I860'  (»/ju£pac  E2CHKONTA — 'threescore  or  sixty  days  ' — 'I 
have  appointed  each  "  DAT  "  for  a  "  YEAR,"  '    Ezek.  iv.  6)  :  and  we  know, 
from  our  '  common  experience,'  how  speedily  such  a  measure  of  time 
will  pass  away. 

No  words  can  be  '  more  explicit '  than  these  of  OUR  BLESSED  LORD  : 
viz.  '  THIS  GOSPEL  of  the  Kingdom  shall  be  preached  in  ALL  the  EARTH, 
for  a  Witness  to  ALL  NATIONS  ;  AND  THEN,  shall  the  END  COME.'  The 

*  next   18   years '    must   therefore  supply  the  interval  of  the  '  special 
Episcopal  forerunners.' 

(Matt.  xxiv.  14.) 
See  the    '  JEWISH    INTELLIGENCER  '  of  the  present  month  (April) 


216  A   BUDGET   OF  PAKADOXES. 

p.  153,  for  the  *  Debates  in  Parliament,'  respecting  the  BISHOP  OP 
JERUSALEM,  viz.  Dr.  Bowring,  Mr.  Hume,  Sir  R.  Inglis,  Sir  R.  Peel, 
Viscount  Palmerston." 

I  have  quoted  this  at  length,  to  show  the  awful  threats  which 
were  published  at  a  time  of  some  little  excitement  about  the 
phenomenon,  under  the  name  of  the  London  Society.  The 
assumption  of  a  corporate  appearance  is  a  very  unfair  trick  :  and 
there  are  junctures  at  which  harm  might  be  done  by  it. 

Wealth  the  name  and  number  of  the  Beast,  666,  in  the  Book  of 
Revelation.     [By  John  Taylor.]     London,  1844,  8vo. 

Whether  Junius  or  the  Beast  be  the  more  difficult  to  identify, 
jmusi)  be  referred  to  Mr.  Taylor,  the  only  person  who  has  at- 
tempted both.  His  cogent  argument  on  the  political  secret  is 
not  unworthily  matched  in  his  treatment  of  the  theological 
riddle.  He  sees  the  solution  in  svTropia,  which  occurs  in  the 
'Acts  of  the  Apostles  as  the  word  for  wealth  in  one  of  its  most 
.disgusting  forms,  and  makes  666  in  the  most  straightforward 
way.  This  explanation  has  as  good  a  chance  as  any  other.  The 
work  contains  a  general  attempt  at  explanation  of  the  Apoca- 
lypse, and  some  history  of  opinion  on  the  subject.  It  has  not 
sthe  prolixity  which  is  so  common  a  fault  of  apocalyptic  com- 
mentators. 

A  practical  Treatise  on  Eclipses  .  .  .  with  remarks  on  the  anom- 
alies of  the  present  Theory  of  the  Tides.    By  T.  Kerigan,  F.R.S. 

1844,  8vo. 

Containing  also  a  refutation  of  the  theory  of  the  tides,  and  after- 
wards increased  by  a  supplement,  '  Additional  facts  and  argu- 
ments against  the  theory  of  the  tides,'  in  answer  to  a  short  notice 
in  the  Athenceum  journal.  Mr.  Kerigan  was  a  lieutenant  in  the 
Navy:  he  obtained  admission  to  the  Royal  Society  just  before 
the  publication  of  his  book. 

A  new  theory  of  Gravitation.      By  Joseph  Denison,  Esq.    London, 

1844,  12mo. 
Commentaries  on  the  Principia.     By  the  author  of  '  A  new  theory 

of  Gravitation.'     London,  1846,  8vo. 

Honour  to  the  speculator  who  can  be  put  in  his  proper  place 
by  one  sentence,  be  that  place  where  it  may. 

'  But  we  have  shown  that  the  velocities  are  inversely  as  the  square 
roots  of  the  mean  distances  from  the  sun  ;  wherefore,  by  equality  of 
ratios,  the  forces  of  the  sun's  gravitation  upon  them  are  also  inversely 
aa  the  square  roots  of  their  distances  from  the  sun.' 


EASTER  DAY  PARADOXERS.  217 

In  the  years  1818  and  1845  the  full  moon  fell  on  Easter  Day, 
having  been  particularly  directed  to  fall  before  it  in  the  act  for 
the  change  of  style,  and  in  the  English  missals  and  prayer-books 
of  all  time  :  perhaps  it  would  be  more  correct  to  say  that  Easter 
Day  was  directed  to  fall  after  the  full  moon  ;  c  but  the  principle 
is  the  same.'  No  explanation  was  given  in  1818,  but  Easter  was 
kept  by  the  tables,  in  defiance  of  the  rule,  and  of  several  protests. 
A  chronological  panic  was  beginning  in  December  1844,  which 
was  stopped  by  the  Times  newspaper  printing  extracts  from  an 
article  of  mine  in  the  Companion  to  the  Almanac  for  1845,  which 
had  then  just  appeared.  No  one  had  guessed  the  true  reason, 
which  is  that  the  thing  called  the  moon  in  the  Gregorian  Calendar 
is  not  the  moon  of  the  heavens,  but  a  fictitious  imitation  put 
wrong  on  purpose,  as  will  presently  appear,  partly  to  keep  Easter 
out  of  the  way  of  the  Jews'  Passover,  partly  for  convenience  of 
calculation.  The  apparent  error  happens  but  rarely  ;  and  all  the 
work  will  perhaps  have  to  be  gone  over  next  time.  I  now  give 
two  bits  of  paradox. 

Some  theologians  were  angry  at  this  explanation.  A  review 
called  the  Christian  Observer  (of  which  Christianity  I  do  not 
know)  got  up  a  crushing  article  against  me.  I  did  not  look  at  it, 
feeling  sure  that  an  article  on  such  a  subject  which  appeared  on 
January  1,  1845,  against  a  publication  made  in  December  1844, 
must  be  a  second-hand  job.  But  some  years  afterwards  (Sept.  10, 
1850),  the  reviews,  &c.  having  been  just  placed  at  the  disposal  of 
readers  in  the  old  reading-  room  of  the  Museum,  I  made  a  tour  of 
inspection,  came  upon  my  critic  on  his  perch,  and  took  a  look  at 
him.  I  was  very  glad  to  remember  this,  for,  though  expecting 
only  second-hand,  yet  even  of  this  there  is  good  and  bad ;  and 
I  expected  to  find  some  hints  in  the  good  second-hand  of  a 
respectable  clerical  publication.  I  read  on,  therefore,  attentively, 
but  not  long  :  I  soon  came  to  the  information  that  some  additions 
to  Delambre's  statement  of  the  ride  for  finding  Easter,  belonging 
to  distant  years,  had  been  made  by  Sir  Harris  Nicolas !  Now  as  I 
myself  furnished  my  friend  Sir  H.  N.  with  Delambre's  digest  of 
Clavius's  rule,  which  I  translated  out  of  algebra  into  common 
language  for  the  purpose,  I  was  pretty  sure  this  was  the  ignorant 
reading  of  a  person  to  whom  Sir  H.  N.  was  the  highest  ariik- 
metical  authority  on  the  subject.  A  person  pretending  to 
chronology,  without  being  able  to  distinguish  the  historical 
points — so  clearly  as  they  stand  out — in  which  Sir  H.  N.  speaks 
with  authority,  from  the  arithmetical  points  of  pure  reckoning  on 
which  he  does  not  pretend  to  do  more  than  directly  repeat  others, 


213  A   BUDGET   OF  PAEADOXES. 

.must  be  as  fit  to  talk  about  the  construction  of  Easter  Tables  as 
the  Spanish  are  to  talk  French.  I  need  hardly  say  that  the 
additions  for  distant  years  are  as  much  from  Clavius  as  the  rest : 
my  reviewer  was  not  deep  enough  in  his  subject  to  know  that 
Clavius  made  and  published,  from  his  rules,  the  full  table  up  to 
A.D.  5000,  for  all  the  moveable  feasts  of  every  year !  I  gave  only 
a  glance  at  the  rest :  I  found  I  was  either  knave  or  fool,  with  a 
leaning  to  the  second  opinion ;  and  I  came  away  satisfied  that  my 
critic  was  either  ignoramus  or  novice,  with  a  leaning  to  the  first. 
I  afterwards  found  an  ambiguity  of  expression  in  Sir  H.  N.'s 
account — whether  his  or  mine  I  could  not  tell — which  might 
mislead  a  novice  or  content  an  ignoramus,  but  would  have  been 
properly  read  or  further  inquired  into  by  a  competent  person. 

The  second  case  is  this.  Shortly  after  the  publication  of  my 
article,  a  gentleman  called  at  my  house,  and,  finding  I  was  not  at 
home,  sent  up  his  card — with  a  stylish  west-end  club  on  it — to 
my  wife,  begging  for  a  few  words  on  pressing  business.  With 
many  well-expressed  apologies,  he  stated  that  he  had  been  alarmed 
by  hearing  that  Prof.  De  M.  had  an  intention  of  altering  Easter 
next  year.  Mrs.  De  M.  kept  her  countenance,  and  assured  him 
that  I  had  no  such  intention,  and  further,  that  she  greatly 
doubted  my  having  the  power  to  do  it.  Was  she  quite  sure? 
his  authority  was  very  good :  fresh  assurances  given.  He  was 
greatly  relieved,  for  he  had  some  horses  training  for  after  Easter, 
which  would  not  be  ready  to  run  if  it  were  altered  the  wrong 
way.  A  doubt  comes  over  him  :  would  Mrs.  De  M.,  in  the  event 
;  of  her  being  mistaken,  give  him  the  very  earliest  information  ? 
Promise  given ;  profusion  of  thanks ;  more  apologies ;  and  de- 
parture. 

Now,  candid  reader ! —  or  uncandid  either  ! — which  most 
deserves  to  be  laughed  at  ?  A  public  instructor,  who  undertakes 
to  settle  for  the  world  whether  a  reader  of  Clavius,  the  constructor 
of  the  Gregorian  Calendar,  is  fool  or  knave,  upon  information 
derived  from  a  compiler — in  this  matter — of  his  own  day;  or  a 
gentleman  of  horse  and  dog  associations  who,  misapprehending 
something  which  he  heard  about  a  current  topic,  infers  that  the 
reader  of  Clavius  had  the  ear  of  the  Government  on  a  proposed 
alteration.  I  suppose  the  querist  had  heard  some  one  say, 
perhaps,  that  the  day  ought  to  be  set  right,  and  some  one  else 
remark  that  I  might  be  consulted,  as  the  only  person  who  had 
discussed  the  matter  from  the  original  source  of  the  Calendar. 

To  give  a  better  chance  of  the  explanation  being  at  once 
produced,  next  time  the  real  full  moon  and  Easter  Day  shall  fall 


THE   EASTER   QUESTION.'  219 

together,  I  insert  here  a  summary  which  was  printed  in  the  Irish 
Prayer-book  of  the  Ecclesiastical  Society.  If  the  amusement 
given  by  paradoxers  should  prevent  a  useless  discussion  some  years 
hence,  I  and  the  paradoxers  shall  have  done  a  little  good  between 
us — at  any  rate,  I  have  done  my  best  to  keep  the  heavy  weight 
afloat  by  tying  bladders  to  it.  I  think  the  next  occurrence  will 
be  in  1875. 

EASTER   DAY. 

In  the  years  1818  and  1845,  Easter  Day,  as  given  by  the  rules  in 
24  Geo.  II.  cap.  23.  (known  as  the  act  for  the  change  of  style)  contra- 
dicted the  precept  given  in  the  preliminary  explanations.  The  precept 
is  as  follows  : — 

'  Easter  Day,  on  which  the  rest '  of  the  moveable  feasts  '  depend,  is 
always  the  First  Sunday  after  the  Full  Moon,  which  happens  upon  or 
next  after  the  Twenty-first  Day  of  March  ;  and  if  the  Full  Moon  hap- 
pens upon  a  Sunday,  Easter  Day  is  the  Sunday  after.' 

But  in  1818  and  1845,  the  full  moon  fell  on  a  Sunday,  and  yet  the 
rules  gave  that  same  Sunday  for  Easter  Day.  Much  discussion  was 
produced  by  this  circumstance  in  1818  :  but  a  repetition  of  it  in  1845 
was  nearly  altogether  prevented  by  a  timely l  reference  to  the  inten- 
tion of  those  who  conducted  the  Gregorian  reformation  of  the  Calendar. 
Nevertheless,  seeing  that  the  apparent  error  of  the  Calendar  is  due  to 
the  precept  in  the  Act  of  Parliament,  which  is  both  erroneous  and  in- 
sufficient, and  that  the  difficulty  will  recur  so  often  as  Easter  Day  falls 
on  the  day  of  full  moon,  it  may  be  advisable  to  select  from  the  two 
articles  cited  in  the  note  sucb  of  their  conclusions  and  rules,  without 
proof  or  controversy,  as  will  enable  the  reader  to  understand  the  main 
points  of  the  Easter  question,  and,  should  he  desire  it,  to  calculate  for 
himself  the  Easter  of  the  old  or  new  style,  for  any  given  year. 

] .  In  the  very  earliest  age  of  Christianity,  a  controversy  arose  as 
to  the  mode  of  keeping  Easter,  some  desiring  to  perpetuate  the  Passover, 
others  to  keep  the  festival  of  the  Resurrection.  The  first  afterwards 
obtained  the  name  of  Quartadecimans,  from  their  Easter  being  always 
kept  on  ike  fourteenth  day  of  the  moon  (Exod.  xii.  18,  Levit.  xxiii.  5.). 
But  though  it  is  unquestionable  that  a  Judaizing  party  existed,  it  is 
also  likely  that  many  dissented  on  chronological  grounds.  It  is  clear 
that  no  perfect  anniversary  can  take  place,  except  when  the  fourteenth 

1  In  the  Companion  to  the  Almanac  for  1845  is  a  paper  by  Professor  De  Morgan, 
'  On  the  Ecclesiastical  Calendar,'  the  statements  of  which,  so  far  as  concerns  the 
Gregorian  Calendar,  are  taken  direct  from  the  work  of  Clavius,  the  principal  agent  in 
the  arrangement  of  the  reformed  reckoning.  This  was  followed,  in  the  Companion  to 
the  Almanac  for  1846,  by  a  second  paper,  by  the  same  author,  headed  'On  the  Earliest 
Printed  Almanacs,'  much  of  which  is  written  in  direct  supplement  to  the  former 
article. 


220  A   BUDGET   OF  PARADOXES. 

of  the  moon,  and  with  it  the  passover,  falls  on  a  Friday.  Suppose,  for 
instance,  it  falls  on  a  Tuesday :  one  of  three  things  must  be  done. 
Either  (which  seems  never  to  have  been  proposed)  the  crucifixion  and 
resurrection  must  be  celebrated  on  Tuesday  and  Sunday,  with  a  wrong 
interval ;  or  the  former  on  Tuesday,  the  latter  on  Thursday,  aban- 
doning the  first  day  of  the  week  ;  or  the  former  on  Friday,  and  the 
latter  on  Sunday,  abandoning  the  paschal  commemoration  of  the 
crucifixion. 

The  last  mode  has  been,  as  every  one  knows,  finally  adopted.  The 
disputes  of  the  first  three  centuries  did  not  turn  on  any  calendar 
questions.  The  Easter  question  was  merely  the  symbol  of  the  strug- 
gle between  what  we  may  call  the  Jewish  and  Gentile  sects  of 
Christians  :  and  it  nearly  divided  the  Christian  world,  the  Easterns, 
for  the  most  part,  being  Quartadecimans.  It  is  very  important  to 
note  that  there  is  no  recorded  dispute  about  a  method  of  predicting  the 
new  moon,  that  is,  no  general  dispute  leading  to  formation  of  sects : 
there  may  have  been  difficulties,  and  discussions  about  them.  The 
Metonic  cycle,  presently  mentioned,  must  have  been  used  by  many, 
perhaps  most,  churches. 

2.  The  question  came  before  the  Nicene  Council  (A.D.  325)  not 
as  an  astronomical,  but  as  a  doctrinal,  question :  it  was,  in  fact,  this, 
Shall  the  passover  l  be  treated  as  a  part  of  Christianity  ?  The  Council 
resolved  this  question  in  the  negative,  and  the  only  information  on  its 
premises  and  conclusion,  or  either,  which  comes  from  itself,  is  contained 
in  the  following  sentence  of  the  synodical  epistle,  which  epistle  is  pre- 
.  served  by  Socrates  and  Theodoret.  '  We  also  send  you  the  good  news 
concerning  the  unanimous  consent  of  all  in  reference  to  the  celebration 
of  the  most  solemn  feast  of  Easter,  for  this  difference  also  has  been 
made  up  by  the  assistance  of  your  prayers  :  so  that  all  the  brethren  in 
the  East,  who  formerly  celebrated  this  festival  at  the  same  time  as  the 
Jews,  will  in  future  conform  to  the  Romans  and  to  us,  and  to  all  who 
have  of  old  observed  our  manner  of  celebrating  Easter.'  This  is  all 
that  can  be  found  on  the  subject :  none  of  the  stories  about  the  Coun- 
cil ordaining  the  astronomical  mode  of  finding  Easter,  and  introducing 
the  Metonic  cycle  into  ecclesiastical  reckoning,  have  any  contemporary 
evidence :  the  canons  which  purport  to  be  those  of  the  Nicene  Council 
do  not  contain  a  word  about  Easter  ;  and  this  is  evidence,  whether  we 
suppose  those  canons  to  be  genuine  or  spurious. 

3.  The  astronomical  dispute  about  a  lunar  cycle  for  the  predic- 
tion of  Easter  either  commenced,  or  became  prominent,  by  the  ex- 
tinction of  greater  ones,  soon  after  the  time  of  the  Nicene  Council. 
Pope  Innocent  I.  met  with  difficulty  in  414.  S.  Leo,  in  454,  ordained 
that  Easter  of  455  should  be  April  24 ;  which  is  right.  It  is  useless  to 

1  It  may  be  necessary  to  remind  some  English  readers  that  in  Latin  and  its  derived 
European  languages,  -what  we  call  Easter  is  called  the  passover  (pascha).  The 
Quartadecimans  had  the  name  on  their  side :  a  possession  which  often  is,  in  this  world, 
nine  points  of  the  law. 


THE  EASTEK  QUESTION.  221 

record  details  of  these  disputes  in  a  snmmary :  the  result  was,  that  in 
the  year  463,  Pope  Hilarius  employed  Victorinus  of  Aquitaine  to 
correct  the  Calendar,  and  Victorinus  formed  a  rule  which  lasted  until 
the  sixteenth  century.  He  combined  the  Metonic  cycle  and  the  solar 
cycle,  presently  described.  But  this  cycle  bears  the  name  of  Dionysius 
Exiguus,  a  Scythian  settled  at  Rome,  about  A.D.  530,  who  adapted 
it  to  his  new  yearly  reckoning,  when  he  abandoned  the  eera  of  Dio- 
cletian as  a  commencement,  and  constructed  that  which  is  now  in 
common  use. 

4.  With  Dionysius,  if  not  before,  terminated  all  difference  as   to 
the  mode  of  keeping  Easter  which  is  of  historical  note  :  the  increasing 
defects  of  the   Easter  Cycle  produced   in  time  the  remonstrance  of 
persons  versed  in  astronomy,  among  whom  may  be  mentioned  Roger 
Bacon,   Sacrobosco,   Cardinal  Cusa,   Regiomontanus,    &c.      Prom  the 
middle  of  the  sixth  to  that  of  the  sixteenth  century,  one  rule  was 
observed. 

5.  The  mode  of  applying   astronomy   to    chronology  has   always 
involved   these    two   principles.      First,   the   actual    position   of    the 
heavenly  body  is  not  the  object  of  consideration,  but  what  astronomers 
call  its  mean  place,  which  may  be  described  thus.     Let  a  fictitious  sun 
or  moon  move  in  the  heavens,  in  such  manner  as  to  revolve  among  the 
fixed  stars  at  an  average  rate,  avoiding  the  alternate  accelerations  and 
retardations  which  take  place  in  every  planetary  motion.     Thus  the 
fictitious   (say  mean)   sun  and  moon  are  always  very  near  to  the  real 
sun  and  moon.     The  ordinary  clocks  show  time  by  the  mean,  not  the 
real,  sun :  and  it  was  always  laid  down  that  Easter  depends  on  the 
opposition  (or  full  moon)  of  the  mean  sun  and  moon,  not  of  the  real 
ones.     Thus  we  see  that,  were  the  Calendar  ever  so  correct  as  to  the 
mean  moon,  it  would  be  occasionally  false  as  to  the  true  one  :  if,  for 
instance,  the  opposition  of  the  mean  sun  and  moon  took  place  at  one 
second  before  midnight,  and  that  of  thet  real  bodies  only  two  seconds 
afterwards,  the  calendar  day  of  full  moon  would  be  one  day  before 
that  of  the  common  almanacs.     Here  is  a  way  in  which  the  discussions 
of  1818  and  1845  might  have  arisen:  the  British  legislature   has  de- 
fined the  moon  as  the  regulator  of  the  paschal  calendar.     But  this  was 
only  a  part  of  the  mistake. 

6.  Secondly,  in  the  absence  of  perfectly  accurate  knowledge  of  the 
solar  and  lunar  motion  (and  for  convenience,  even  if  such  knowledge 
existed),  cycles  are,  and  always  have   been   taken,  which   serve   to 
represent  those  motions  nearly.     The  famous  Metonic  cycle,  which  is 
introduced  into  ecclesiastical  chronology  under  the  name  of  the  cycle 
of  the  golden  numbers,  is  a  period  of  19  Julian1  years.     This  period, 
in   the  old  Calendar,  was  taken  to  contain  exactly  235  lunations,  or 
intervals  between  new  moons,  of  the  mean  moon.     Now  the  state  of 
the  case  is  this  : — 

1  The  Julian  year  is  a  year  of  the  Julian  Calendar,  in  which  there  is  leap  year  every 
fourth  year.     Its  average  length  is  therefore  365  days  and  a  quarter. 


222  A   BUDGET   OF  PAEADOXES. 

19  average  Julian  years  make  6939  days  18  hours. 

235  average  lunations  make  6939  days  16  hours  31  minutes. 

So  that  successive  cycles  of  golden  numbers,  supposing  the  first  to 
start  right,  amount  to  making  the  new  moons  fall  too  late,  gradually, 
so  that  the  mean  moon  of  this  cycle  gains  1  hour  29  minutes  in  19 
years  upon  the  mean  moon  of  the  heavens,  or  about  a  day  in  300 
years.  When  the  Calendar  was  reformed,  the  calendar  new  moons 
were  four  days  in  advance  of  the  mean  moon  of  the  heavens :  so  that, 
for  instance,  calendar  full  moon  on  the  18th  usually  meant  real  full 
moon  on  the  14th. 

7.  If    the    difference   above   had   not   existed,  the   moon   of    the 
heavens  (the  mean  moon  at  least),  would  have  returned  permanently 
to  the  same  days  of  the  month  in  19  years ;  with   an  occasional  slip 
arising  from  the   unequal  distribution  of  the  leap  years,  of  which  a 
period  contains  sometimes  five  and  sometimes  four.     As  a  general  rule, 
the  days  of  new  and  full  moon  in  any  one  year  would  have  been  also 
the  days  of  new  and  full  moon  of  a  year  having  19  more  units  in  its 
date.     Again,  if  there  had  been  no  leap  years,  the  days  of  the  month 
would  have  returned  to  the  same  days  of  the  week  every  seven  years. 
The  introduction  of  occasional  29ths  of  February  disturbs  this,  and 
makes  the  permanent  return  of  month  days  to  week  days  occur  only 
after  28  years.     If  all  had  been  true,  the  lapse  of  28  times  19,  or  532 
years,  would  have  restored  the  year  in  every  point :  that  is,  A.D.  1,  for 
instance,  and  A.D.   538,  would  have  had  the  same  almanac  in  every 
matter  relating  to  week  days,  month  days,  sun,  and  moon  (mean  sun 
and  moon  at  least).     And  on  the  supposition  of  its  truth,  the  old 
system  of  Dionysius  was  framed.     Its  errors  are,  first,  that  the  mo- 
ments of  mean  new  moon  advance  too  much  by  Ih.  29m.  in  19  average 
Julian  years ;  secondly,  that  the  average  Julian  year  of  365^  days  is 
too  long  by  llm.  10s. 

8.  The   Council  of  Trent,  moved  by  the  representations  made  on 
the  state  of  the  Calendar,  referred  the  consideration  of  it  to  the  Pope- 
In  1577,  Gregory  XIII.  submitted  to  the  Roman  Catholic  Princes  and 
Universities  a  plan  presented  to  him  by  the  representatives  of  Aloysius 
Lilius,  then  deceased.     This  plan  being  approved  of,  the  Pope  nomi 
nated  a  commission  to  consider  its  details,  the  working  member  of 
which  was  the  Jesuit  Clavius.     A  short  work  was  prepared  by  Clavius, 
descriptive  of  the  new   Calendar:  this  was  published1  in  1582,  with 
the  Pope's  bull  (dated  February  24,  1581)  prefixed.     A  larger  work 
was  prepared  by  Clavius,  containing  fuller  explanation,  and  entitled 
'  Romani  Calendarii  a  Gregorio  XIII.  Pontifice  Maximo  restituti  Ex- 
plicatio.'     This  was  published  at  Rome  in  1603,  and  again  in  the  col- 
lection of  the  works  of  Clavius  in  1612. 

1  The  title  of  this  work,  which  is  the  authority  on  all  points  of  the  new  Calendar,  is 
1  Kalendarium  Gregorianum  Perpetuum.  Cum  Privilegio  Summi  Pontificis  Et  Alio- 
rum  Principum.  Komse,  Ex  Officina  Dominici  Basse.  MDLXXXII.  Cum  Licentia, 
Superiorum '  (quarto,  pp.  60). 


THE  EASTER  QUESTION.    '  223 

9.  The  following  extracts  from  Clavius  settle  the  question  of  the-' 
meaning  of  the  term  moon,  as  used  in  the  Calendar  : — 

*  Who,  except  a  few  who  think  they  are  very  sharp-sighted  in  this 
matter,  is  so  blind  as  not  to  see  that  the  14th  of  the  moon  and  the  full 
moon  are  not  the  same  things  in  the  Church  of  God  ?  .  .  .  Although 
the  Church,  in  finding  the  new  moon,  and  from  it  the  14th  day,  uses 
neither  the  true  nor  the  mean  motion  of  the  moon,  but  measures  only 
according  to  the  order  of  a  cycle,  it  is  nevertheless  undeniable  that 
the  mean  full  moons  found  from  astronomical  tables  are  of  the  greatest 
use  in  determining  the  cycle  which  is  to  be  preferred  .  .  .  the  new 
moons  of  which  cycle,  in  order  to  the  due  celebration  of  Easter,  should 
be  so  arranged  that  the  14th  days  of  those  moons,  reckoning  from  the 
day  of  new  moon  inclusive,  should  not  fall  two  or  more  days  before  the 
mean  full  moon,  but  only  one  day,  or  else  on  the  very  day  itself,  or 
not  long  after.  And  even  thus  far  the  Church  need  not  take  very 
great  pains  ...  for  it  is  sufficient  that  all  should  reckon  by  the  14th 
day  of  the  moon  in  the  cycle,  even  though  sometimes  it  should  be  more 
than  one  day  before  or  after  the  mean  full  moon  .  .  .  We  have  taken 
pains  that  in  our  cycle  the  new  moons  should  follow  the  real  new 
moons,  so  that  the  14th  of  the  moon  should  fall  either  the  day  before 
the  mean  full  moon,  or  on  that  day,  or  not  long  after ;  and  this  was 
done  on  purpose,  for  if  the  new  moon  of  the  cycle  fell  on  the  same  day 
as  the  mean  new  moon  of  the  astronomers,  it  might  chance  that  we 
should  celebrate  Easter  on  the  same  day  as  the  Jews  or  the  Quarta- 
deciman  heretics,  which  would  be  absurd,  or  else  before  them,  which 
would  be  still  more  absurd.' 

From  this  it  appears  that  Clavius  continued  the  Calendar  of  his 
predecessors  in  the  choice  of  the  fourteenth  day  of  the  moon.  Our 
legislature  lays  down  the  day  of  the  full  moon :  and  this  mistake 
appears  to  be  rather  English  than  Protestant ;  for  it  occurs  in  missals 
published  in  the  reign  of  Queen  Mary.  The  calendar  lunation  being 
29^  days,  the  middle  day  is  the  fifteenth  day,  and  this  is  and  was 
reckoned  as  the  day  of  the  full  moon.  There  is  every  right  to  presume 
that  the  original  passover  was  a  feast  of  the  real  full  moon :  but  it  is 
most  probable  that  the  moons  were  then  reckoned,  not  from  the  astro- 
nomical conjunction  with  the  sun,  which  nobody  sees  except  at  an 
eclipse,  but  from  the  day  of  first  visibility  of  the  new  moon.  In  fine 
climates  this  would  be  the  day  or  two  days  after  conjunction ;  and  the 
fourteenth  day  from  that  of  first  visibility  inclusive,  would  very  often 
be  the  day  of  full  moon.  The  following  is  then  the  proper  correction 
of  the  precept  in  the  Act  of  Parliament : — 

Easter  Day,  on  which  the  rest  depend,  is  always  the  First  Sunday 
after  the  fourteenth  day  of  the  calendar  moon  which  happens  upon  or 
next  after  the  Twenty-first  day  of  March,  according  to  the  rules  laid 
down  for  the  construction  of  the  Calendar ;  and  if  the  fourteenth  day 
happens  upon  a  Sunday,  Easter  Day  is  the  Sunday  after. 

10.     Further,  it  appears  that  Clavius  valued  the  celebration  of  the 


224  A   BUDGET  OF  PARADOXES. 

festival  after  the  Jews,  &c.,  more  than  astronomical  correctness.  He 
gives  comparison  tables  which  would  startle  a  believer  in  the  astrono- 
mical intention  of  his  Calendar :  they  are  to  show  that  a  calendar  in 
which  the  moon  is  always  made  a  day  older  than  by  him,  represents  the 
heavens  better  than  he  has  done,  or  meant  to  do.  But  it  must  be  ob- 
served that  this  diminution  of  the  real  moon's  age  has  a  tendency  to 
make  the  English  explanation  often  practically  accordant  with  the 
Calendar.  For  the  fourteenth  day  of  Clavius  is  generally  the  fifteenth 
day  of  the  mean  moon  of  the  heavens,  and  therefore  most  often  that  of 
the  real  moon.  But  for  this,  1818  and  1845  would  not  have  been  the 
only  instances  of  our  day  in  which  the  English  precept  would  have 
contradicted  the  Calendar. 

11.  In  the  construction  of  the  Calendar,  Clavius  adopted  the  ancient 
cycle  of  532  years,  but,  we  may  say,  without  ever  allowing  it  to  run 
out.     At  certain  periods,  a  shift  is  made  from  one  part  of  the  cycle 
into  another.     This  is  done  whenever  what  should  be  Julian  leap  year 
is  made  a  common  year,  as  in  1700,  1800,  1900,  2100,  &c.     It  is  also 
done  at  certain  times  to  correct  the  error  of  Ih.  19m.,  before  referred 
to,  in  each  cycle  of  golden  numbers :  Clavius,  to  meet  his  view  of  the 
amount  of  that  error,  put  forward  the  moon's  age  a  day  8  times  in 
2,500  years.     As  we  cannot  enter  at  full  length  into  the  explanation, 
we  must  content  ourselves  with  giving  a  set  of  rules,  independent  of 
tables,  by  which  the  reader  may  find  Easter  for  himself  in  any  year, 
either  by  the  old  Calendar  or  the  new.     Any  one  who  has  much  oc- 
casion to  find  Easters  and  moveable  feasts  should  procure  Francoaur's !- 
tables. 

1 2.  Rule  for  determining  Easter  Day  of  the  Gregorian  Calendar  in  any 
year  of  the  new  style.     To  the  several  parts  of  the  rule  are  annexed,  by 
way  of  example,  the  results  for  the  year  1849. 

I.  Add  1  to  the  given  year.     (1850). 

II.  Take  the  quotient  of  the  given  year  divided  by  4,  neglecting  the  remainder. 
(462). 

III.  Take  16  from  the  centurial  figures  of  the  given  year,  if  it  can  be  done,  and 

take  the  remainder.     (2). 

IV.  Take  the  quotient  of  III.  divided  by  4,  neglecting  the  remainder.     (0). 
V.  From  the  sum  of  I.,  II.,  and  IV.,  substract  III.     (2310). 

VI.  Find  the  remainder  of  V.  divided  by  7.     (0). 

VII.  Subtract  VI.  from  7  ;  this  is  the  number  of  the  dominical  letter  ^  ?  9  ?  ?F  ? 

I«oo4oo7« 
(7;  dominical  letter  Q-). 

VIII.  Divide  I.  by  19,  the  remainder  (or  19,  if  no  remainder)  is  the  golden  number. 
(7). 

1  '  Manuels-Roret.  Theorie  du  Calendrier  et  collection  de  tous  les  Calendriers  des 
Annees  passees  et  futures. . .  .Par  L.  B.  Francoeur, . .  .Paris,  a  la  librairie  encyclope- 
dique  de  Roret,  rue  Hautefeuille,  10  bis.  1842.'  (12mo.)  In  this  valuable  manual, 
the  35  possible  almanacs  are  given  at  length,  with  such  preliminary  tables  as  will 
enable  any  one  to  find,  by  mere  inspection,  which  almanac  he  is  to  choose  for  any 
year,  whether  of  old  or  new  style.  [1866.  I  may  now  refer  to  my  own  'Book  of 
Almanacs,'  for  the  same  purpose]. 


RULE   FOR   FINDING   EASTER   DAY. 


225 


IX.  From  the  centurial  figures  of  the  year  subtract  17,  divide  by  25,  and  keep  the 

quotient.     (0). 

X.  Subtract  IX.  and  15  from  the  centurial  figures,  divide  by   3,  and  keep  the 
quotient.     (1). 

XI.  To  VIII.  add  ten  times  the  next  less  number,  divide  by  30,  and  keep  the 

remainder.     (7). 

XII.  To  XI.  add  X.  and  IV.,  and  take  away  III.,  throwing  out  thirties,  if  any.  If 
this  give  24,  change  it  into  25.  If  25,  change  it  into  26,  whenever  the 
golden  number  is  greater  than  11.  If  0,  change  it  into  30.  Thus  we  have 
the  epact,  or  age  of  the  Calendar  moon  at  the  beginning  of  tho  year.  (6). 

When  the  Epact  is  23,  or  less.  \         When  the  Epact  is  greater  than  23. 

XIII.  Subtract  XII.,  the  epact,  from  45.       XIU.  Subtract   XII.,    the    epact,    from 


(39). 

XIV.  Subtract  the  epact  from  27,  divide 
by  7,  and  keep  the  remainder,  or 
7,  if  there  be  no  remainder.  (7). 


75. 

XIV.  Subtract  the  epact  from  57,  divide 
by  7,  and  keep  the  remainder, 
or  7,  if  there  be  no  remainder. 


XV.  To  XIII.  add  VII.,  the  dominical  number,  (and  7  besides,  if  XIV.  be  greater 
than  VII.,)  and  subtract  XIV.,  the  result  is  the  day  of  March,  or  if  more 
than  31,  subtract  31,  and  the  result  is  the  day  of  April,  on  which  Easter 
Sunday  falls.  (39 ;  Easter  Day  is  April  8). 

In  the  following  examples,  the  several  results  leading  to  the  final  con- 
clusion are  tabulated. 


Given  year 

1592 

1637 

1723 

1853 

2018 

4686 

I. 

1593 

1638 

1724 

1854 

2019 

4687 

II. 

398 

409 

430 

463 

504 

1171 

III. 

— 

0 

1 

2 

4 

30 

IV. 

— 

0 

0 

0 

1 

r    7 

V. 

1991 

2047 

2153 

2315 

2520 

5835 

VI. 

3 

3 

4 

5 

0 

4 

VII. 

4 

4 

3 

2 

7 

3 

VIII. 

16 

4 

14 

11 

5 

13 

IX. 

— 

— 

0 

0 

0 

1 

X. 

0 

0 

0 

1 

1 

10 

XI. 

16 

4 

24 

21 

15 

13 

XII. 

16 

4 

23 

20 

13 

0  say  30 

XIII. 

29 

41 

22 

25 

32 

45 

XIV. 

4 

2 

4 

7 

7 

6 

XV. 

29 

43 

28 

27 

32 

49 

Easter  Day. 

Mar.  29 

Apr.  12 

Mar.  28 

Mar.  27 

Apr.  1 

Apr.  18 

13.  Stile  for  determining  Easter  Day  of  the  Antegregorian  Calendar  in 
any  year  of  the  old  style.  To  the  several  parts  of  the  rule  are  annexed, 
by  way  of  example,  the  results  for  the  year  1287.  The  steps  are 
numbered  to  correspond  with  the  steps  of  the  Gregorian  rule,  so  that 
it  can  be  seen  what  augmentations  the  latter  requires. 

I.  Set  down  the  given  year.     (1287). 

II.  Take  the  quotient  of  the  given  year  divided  by  4,  neglecting  the  remainder 
(321). 

V.  Take  4  more  than  the  sum  of  I.  and  II.     (1612). 
VI.  Find  the  remainder  of  V.  divided  by  7.     (2). 

VII.  Subtract  VI.  from  7  ;  this  is  the  number  of  the  dominical  letter 
(5  ;  dominical  letter  E), 

Q 


- 

o  4  o  6  7 


226  A  BUDGET  OF  PAEADOXES. 

VIII.  Divide  one  more  than  the  given  year  by  19,  the  remainder  (or  19  if  no  re- 
mainder) is  the  golden  number.  (15). 

XII.  Divide  3  less  than  11  times  VIII.  by  30  ;  the  remainder  (or  30  if  there  be  no 
remainder)  is  the  epact.  (12). 


When  the  Epact  is  23,  or  less, 

XIII.  Subtract  XII.,  the  epact,  from  45. 

(33). 

XIV.  Subtract  the  epact,  from  27,  divide 

by  7,  and  keep  the  remainder,  or 
7,  if  there  be  no  remainder.  (1). 


When  the  Epact  is  greater  than  23. 

XIII.  Subtract    XII.,    the   epact,  from 

75. 

XIV.  Subtract  the  epact  from  57,  divide 

by  7,  and  keep  the  remainder, 
or  7,  if  there  be  no  remainder. 


XV.  To  XIII.  add  VII.,  the  dominical  number,  (and  7  besides  if  XIV.  be  greater 
than  VII.,)  and  subtract  XIV.,  the  result  is  the  day  of  March,  or  if  more 
than  31,  subtract  31,  and  the  result  is  the  day  of  April,  on  which  Easter 
Sunday  (old  style)  falls.  (37  ;  Easter  Day  is  April  6). 

These  rules  completely  represent  the  old  and  new  Calendars,  so  far 
as  Kaster  is  concerned.  For  further  explanation  we  must  refer  to  the 
articles  cited  at  the  commencement. 

The  annexed  is  the  table  of  new  and  full  moons  of  the 
Gregorian  Calendar,  cleared  of  the  errors  made  for  the  purpose 
of  preventing  Easter  from  coinciding  with  the  Jewish  Passover. 

The  second  table  (page  228)  contains  epacts,  or  ages  of  the 
moon  at  the  beginning  of  the  year  :  thus  in  191  3,  the  epact  is  22  : 
in  1868  it  is  6.  This  table  goes  from  1850  to  1999  :  should  the 
New  Zealander  not  have  arrived  by  that  time,  and  should  the 
churches  of  England  and  Rome  then  survive,  the  epact  table  may 
be  continued  from  their  liturgy-books.  The  way  of  using  the  table 
is  as  follows  :  Take  the  epact  of  the  required  year,  and  find  it 
in  the  farst  or  last  column  of  the  first  table,  in  line  with  it  are 
seen  the  calendar  days  of  new  and  full  moon.  Thus,  when  the 
epact  is  17,  the  new  and  full  moons  of  March  fall  on  the  13th 
and  28th.  The  result  is,  for  the  most  part,  correct :  but  in  a 
minority  of  cases  there  is  an  error  of  a  day.  When  this  happens, 
the  error  is  almost  always  a  fraction  of  a  day  much  less  than 
twelve  hours.  Thus,  when  the  table  gives  full  moon  on  the  27th, 
and  the  real  truth  is  the  28th,  we  may  be  sure  it  is  early  on 
the  28th.  For  example,  the  year  1867.  The  epact  is  25,  and 
we  find  in  the  table  : 

J.          F.    M.        Ap.    M.         Ju.      Jl,        Au.      S.  0.      N.      D. 

New.     .     .      5+      4       5+4       3+2     1,31     29     28-     27     26     25 
Full  ...    20       19-20       19-18         17    16       15     13-      13     11  +  11 

When  the  truth  is  the  day  after  -f  is  written  after  the  date ; 
when  the  day  before,  —  .  Thus,  the  new  moon  of  March  is  on 
the  6th  ;  the  full  moon  of  April  is  on  the  18th. 


Table  of  New  and  Full  ^^ou». 


Jan. 

Feb. 

Mar. 

Apr. 

May 

June 

July 

A.ug. 

Sep. 

Oct. 

NOT. 

Dec. 

1   (I   H 

27 
13 

29 

14 

27 
13 

27 
12 

25 
11 

25 
10 

23 
9 

22 
7 

21 
7 

20 
5 

ll   \}     1 

»{|S 

26 
12 

28 
13 

26 
12 

26 
11 

24 
10 

24 
9 

22 
8 

21 
6 

20 
6 

19 
4 

]4    }    2 

3{ 

27 
12 

25 
11 

27 
12 

25 
11 

25 
10 

23 
9 

23 
8 

21 

7 

20 
5 

19 
5 

18 
3 

17 
3 

}    3 

4  { 

26 
11 

24 
10 

26 
11 

24 
10 

24 
9 

22 
8 

22 
7 

20 
6 

19 
4 

18 
4 

17 

2 

16 

2,31 

}    * 

5  { 

25 
10 

23 
9 

25 
10 

23 
9 

23 
8 

21 

7 

21 
6 

19 
5 

18 
3 

17 
3 

16 
1 

15 
1,30 

I       e 
/ 

6  { 

24 
9 

22 
8 

2i 
9 

22 
8 

22 
7 

20 
6 

20 
5 

18 
4 

17 
2 

16 

2,31 

15 
30 

29     }     6 

7  { 

23 
8 

21 
7 

23 
8 

21 

7 

21 
6 

19 
5 

19 
4 

17 
3 

16 
1 

15 
1,30 

14 

29 

31}  * 

8  {|  27 

20 
6 

22 

7 

20 
6 

20 
5 

18 
4 

18 
3 

16 
2,31 

15 
30 

14 

29 

13 
28 

SI 

11 

26 

}      8 

9  (|  26 

19 
5 

21 
6 

19 
5 

19 
4 

17 
3 

17 

2 

15 
1.30 

14 

29 

13 
28 

12 
27 

1    9 
J    y 

10  { 

20 
5 

18 
4 

20 
5 

18 
4 

18 
3 

16 
2 

16 
1,31 

1! 
29 

13 
28 

12 

27 

11 
26 

251   |}   10 

11  { 

19 
4 

17 
3 

19 

4 

17 
3 

17 

2 

15 
1,30 

15 

30 

13 

28 

12 

27 

11 
26 

10 
25 

9   \\   11 
24  \j    Ai 

12  {|  '5 

16 
2 

18 
3 

16 
2 

16 
1,31 

14 
29 

14 
29 

12 
27 

11 
26 

10 
25 

9 

24 

23   |}    12 

13  { 

17 
2 

15 
1 

17 
2 

15 
1,30 

15 
30 

13 
28 

13 
28 
12 
27 

11 
26 

10 
25 

9 
24 

8 
23 

7  \\  13 

22      |     *o 

M{ 

16 
1,31 

14 

16 
1,31 

14 
29 

14 

29 

12 
27 

10 

25 

9 
24 

8 
23 

22 

dfe 

15  { 

15 
30 

13 
28 

15 
30 

13 
28 

13 

28 

11 
26 

11 
26 

9 
24 

8 
23 

7 
22 

6 
21 

5 

20 

}  15 

16  { 

14 
29 

12 
27 

14 

29 

12 
27 

12 
27 

10 
25 

10 
25 

8 
23 

7 

22 

6 
21 

5 
20 

4 
19 

}  16 

17  { 

13 

28 

11 
26 

13 

28 

11 
26 

11 
26 

9 
24 

9 
24 

7 

22 

6 

21 

5 
20 

4 
19 

.8  1}  » 

18  {|  J? 

10 
25 

12 
27 

10 
25 

10 
25 

8 
23 

8 
23 

6 

21 

5 
20 

4 
19 

3 
18 

17  |)  18 

19  {|  I2l 

9 
24 

11 

26 

9 
24 

9 
24 

7 
22 

7 
22 

5 

20 

4 
19 

3 

18 

2 
17 

\ll\}  19 

20  { 

10 
25 

8 
23 

10 
25 

8 
23 

8 
23 

6 
21 

6 
21 

4 
19 

3 

18 

2 
17 

1,31 
16 

S  |}  20 

21  { 

9 
24 

7 
22 

9 
24 

7 
22 

7 
22 

5 

20 

5 
20 

3 
18 

2 
17 

1,31 
16 

29 
15 

29 
14 

}  21 

22  (|  23 

6 
21 

8 
23 

6 
21 

6 
21 

4 
19 

4 
19 

'2 
17 

1,30 
16 

30 
15 

28 
14 

28 
13 

}  22 

23  { 

7 
22 

5 

20 

7 
22 

5 
20 

5 

20 

3 

18 

3 

18 

1,31 
16 

29 
15 

29 
14 

27 
13 

g  |}  23 

24  { 

6 

21 

5 

19 

6 
21 

5, 

19 

4 
19 

3 

17 

2 

17 

1,30 
15 

29 
14 

28 
13 

27 
12 

S  |}  24 

25  { 

5 

20 

4 
19 

5 

20 

4 
19 

3 

18 

2 
17 

1,31 
16 

29 
15 

28 
13 

27 
13 

26 
11 

25 
11 

}  25 

26  { 

4 
19 

3 
18 

4 
19 

3 
18 

2 
17 

1,30 
16 

30 
15 

28 
14 

27 
12 

26 
12 

25 
10 

24 
10 

}  26 

27  { 

3 
18 

2 

17 

3 
18 

2 
17 

1,31 
16 

29 
15 

29 
14 

27 
13 

26 
11 

25 
11 

24 
9 

23 
9 

}  27 

28  { 

2 
17 

1 
16 

2 

17 

1,30 
16 

SO 
15 

28 
14 

28 
13 

26 
12 

25 
10 

24 
10 

23 
8 

1  1}  28 

29  { 

1,31 
16 

15 

1,31 
16 

29 
15 

29 
14 

27 

13 

27 
12 

25 
11 

24 
9 

23 
9 

22 
7 

"7  !)  29 

SO  \ 

30 
15 

28 
14 

30 
15 

28 
14 

28 
13 

26 

12 

26 
11 

'24 
10 

23 

8 

22 
8 

21    1  20  |\    «n 

6  |  s_£r«o 

.Tan 

Feb 

Mar 

Apr 

Ma; 

Jun 

•*  Juh 

Ang.i  Sep. 

Oct. 

Nov 

1  Dec 

A  BUDGET   OF  PAEADOXES. 


0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

185 

17 

28 

19 

20 

2 

12 

23 

4 

15 

26 

186 

7 

18 

30 

11 

22 

3 

14 

25 

6 

17 

187 

28 

9 

20 

1 

12 

23 

4 

15 

26 

7 

188 

18 

30 

11 

22 

3 

14 

25 

6 

17 

28 

189 

9 

21 

1 

12 

23 

4 

15 

26 

7 

18 

190 

29 

10 

21 

2 

13 

24 

5 

16 

27 

8 

191 

19 

30 

11 

22 

3 

14 

26 

6 

17 

29 

192 

10 

21 

2 

13 

24 

5 

16 

27 

8 

19 

193 

30 

11 

22 

3 

14 

26 

6 

17 

29 

10 

194 

21 

2 

13 

24 

5 

16 

27 

8 

19 

30 

195 

11 

22 

3 

14 

26 

6 

17 

29 

10 

21 

196 

2 

13 

24 

5 

16 

2  | 

8 

19 

30 

11 

197 

22 

3 

14 

26 

6 

17 

29 

10 

21 

2 

198 

13 

24 

5 

16 

27 

8 

19 

30 

11 

22 

199 

3 

14 

26 

6 

17 

29 

10 

21 

2 

13 

I  now  introduce  a  small  paradox  of  my  own  :  and  as  I  am  not 
able  to  prove  it,  I  am  compelled  to  declare  that  any  one  who 
shall  dissent  must  be  either  very  foolish  or  very  dishonest,  and 
will  make  me  quite  uncomfortable  about  the  state  of  his  soul. 
This  being  settled  once  for  all,  I  proceed  to  say  that  the  necessity 
of  arriving  at  the  truth  about  the  assertions  that  the  Nicene 
Council  laid  down  astronomical  tests  led  me  to  look  at  Fathers, 
Church  histories,  &c.  to  an  extent  which  I  never  dreamed  of 
before.  One  conclusion  which  I  arrived  at  was,  that  the  Nicene 
Fathers  had  a  knack  of  sticking  to  the  question  which  many  later 
councils  could  not  acquire.  In  our  own  day,  it  is  not  permitted 
to  Convocation  seriously  to  discuss  any  one  of  the  points  which 
are  bearing  so  hard  upon  their  resources  of  defence — the  cursing 
clauses  of  the  Athanasian  Creed,  for  example.  And  it  may  be 
collected  that  the  prohibition  arises  partly  from  fear  that  there  - 
is  no  saying  where  a  beginning,  if  allowed,  would  end.  There 
seems  to  be  a  suspicion  that  debate,  once  let  loose,  would  play 
up  old  Trent  with  the  liturgy,  and  bring  the  whole  book  to  book. 
But  if  any  one  will  examine  the  real  Nicene  Creed,  without  the 
augmentation,  he  will  admire  the  way  in  which  the  framers  stuck 
to  the  point,  and  settled  what  they  had  to  decide,  according  to 


EASTER  AND  PASSOVER— CLAVIUS.  .  229 

their  view  of  it.  With  such  a  presumption  of  good  sense  in 
their  favour,  it  becomes  easier  to  believe  in  any  claim  which  may 
be  made  on  their  behalf  to  tact  or  sagacity  in  settling  any  other 
matter.  And  I  strongly  suspect  such  a  claim  may  be  made  for 
them  on  the  Easter  question. 

I  collect  from  many  little  indications,  both  before  and  after 
the  Council,  that  the  division  of  the  Christian  world  into  Judai- 
cal  and  Grentile,  though  not  giving  rise  to  a  sectarian  distinction 
expressed  by  names,  was  of  far  greater  force  and  meaning  than 
historians  prominently  admit.  I  took  note  of  many  indications 
of  this,  but  not  notes,  as  it  was  not  to  my  purpose.  If  it  were 
so,  we  must  admire  the  discretion  of  the  Council.  The  Easter 
question  was  the  fighting  ground  of  the  struggle :  the  Eastern 
or  Judaical  Christians,  with  some  varieties  of  usage  and  meaning, 
would  have  the  Passover  itself  to  be  the  great  feast,  but  taken  in 
a  Christian  sense  ;  the  Western  or  Gentile  Christians,  would  have 
the  commemoration  of  the  Resurrection,  connected  with  the 
Passover  only  by  chronology.  To  shift  the  Passover  in  time, 
under  its  name,  Pascha,  without  allusion  to  any  of  the  force  of 
the  change,  was  gently  cutting  away  the  ground  from  under  the 
feet  of  the  Conservatives.  And  it  was  done  in  a  very  quiet  way :  no 
allusion  to  the  precise  character  of  the  change  ;  no  hint  that  the 
question  was  about  two  different  festivals:  'all  the  brethren  in 
the  East,  who  formerly  celebrated  this  festival  at  the  same  time 
as  the  Jews,  will  in  future  conform  to  the  Romans  and  to  us.* 
The  Judaizers  meant  to  be  keeping  the  Passover  as  a  Christian 
feast :  they  are  gently  assumed  to  be  keeping,  not  the  Passover, 
but  a  Christian  feast ;  and  a  doctrinal  decision  is  quietly,  but 
efficiently,  announced  under  the  form  of  a  chronological  ordin- 
ance. Had  the  Council  issued  theses  of  doctrine,  and  excom- 
municated all  dissentients,  the  rupture  of  the  East  and  West 
would  have  taken  place  earlier  by  centuries  than  it  did.  The 
only  place  in  which  I  ever  saw  any  part  of  my  paradox  ad- 
vanced, was  in  an  article  in  the  Examiner  newspaper,  towards 
the  end  of  1866,  after- the  above  was  written. 

A  story  about  Christopher  Clavius,  the  workman  of  the  new 
Calendar.  I  chanced  to  pick  up  '  Albertus  Pighius  Campensis  de 
sequinoctiorum  solsticiorumque  inventione  ....  Ejusdem  de 
ratione  Paschalis  celebrationis,  De  que  Restitutione  ecclesiastic! 
Kalendarii,'  Paris,  1520,  folio.  On  the  title-page  were  decayed 
words  followed  by  ' .  .  hristophor  .  .  C  .  .  ii,  1556  (or  8),'  the 
last  blank  not  entirely  erased  by  time,  but  showing  the  lower 
halves  of  an  I  and  of  an  a,  and  rather  too  much  room  for  a  v. 
It  looked  very  like  E  Libris  Christopher  i  Clavii  1556.  By  the 


230  A   BUDGET   OF  PARADOXES. 

courtesy  of  some  members  of  the  Jesuit  body  in  London,  I 
procured  a  tracing  of  the  signature  of  Clavius  from  Eome,  and 
the  shapes  of  the  letters,  and  the  modes  of  junction  and  disjunc- 
tion, put  the  matter  beyond  question.  Even  the  extra  space 
was  explained ;  he  wrote  himself  Glaums.  Now  in  1556, 
Clavius  was  nineteen  years  old :  it  thus  appears  probable  that 
the  framer  of  the  Gregorian  Calendar  was  selected,  not  merely 
as  a  learned  astronomer,  but  as  one  who  had  attended  to  the 
calendar,  and  to  works  on  its  reformation,  from  early  youth. 
When  on  the  subject  I  found  reason  to  think  that  Clavius  had 
really  read  this  work,  and  taken  from  it  a  phrase  or  two  and  a 
notion  or  two.  Observe  the  advantage  of  writing  the  baptismal 
name  at  full  length. 

The  discovery  of  a  general  resolution  of  all  superior  finite  equa- 
tions, of  every  numerical  both  algebraick  and  transcendent 
form.  By  A.  P.  Vogel,  mathematician  at  Leipzick.  Leipzick 
and  London,  1845,  8vo. 

This  work  is  written  in  the  English  of  a  German  who  has  not 
mastered  the  idiom :  but  it  is  always  intelligible.  It  professes  to 
solve  equations  of  every  degree  '  in  a  more  extent  sense,  and  till 
to  every  degree  of  exactness.'  The  general  solution  of  equations 
of  all  degrees  is  a  vexed  question,  which  cannot  have  the  mys- 
terious interest  of  the  circle  problem,  and  is  of  a  comparatively 
modern  date.  Mr.  Vogel  announces  a  forthcoming  treatise  in 
which  are  resolved  the  '  last  impossibilities  of  pure  mathematics.' 

Elective  Polarity  the  Universal  Agent.  By  Frances  Barbara 
Burton,  authoress  of  '  Astronomy  familiarized,'  '  Physical  As 
tronomy,'  &c.  London,  1845,  8vo. 

The  title  gives  a  notion  of  the  theory.  The  first  sentence 
states,  that  12,500  years  ago  a  Lyrse  was  the  pole-star,  and 
attributes  the  immense  magnitude  of  the  now  fossil  animals  to  a 
star  of  such  'polaric  intensity  as  Vega  pouring  its  magnetic 
streams  through  our  planet.'  Miss  Burton  was  a  lady  of  property, 
and  of  very  respectable  acquirements,  especially  in  Hebrew  ;  she 
was  eccentric  in  all  things. 

1867. — Miss  Burton  is  revived  by  the  writer  of  a  book  on 
meteorology  which  makes  use  of  the  planets :  she  is  one  of  his 
leading  minds. 

In  the  year  1 845  the  old  Mathematical  Society  was  merged  in 
the  Astronomical  Society.  The  circle-squarers,  &c.,  thrive  more 


SPECULATIVE   THOUGHT   IN   ENGLAND.  231 

in  England  than  in  any  other  country :  there  are  most  weeds 
where  there  is  the  largest  crop.  Speculation,  though  not  en- 
couraged by  our  Government  so  much  as  by  those  of  the  Conti- 
nent, has  had,  not  indeed  such  forcing,  but  much  wider  diffusion  : 
few  tanks,  but  many  rivulets.  On  this  point  I  quote  from  the 
preface  to  the  reprint  of  the  work  of  Ramchundra,  which  I 
superintended  for  the  late  Court  of  Directors  of  the  East  India 
Company. — 

'  That  sound  judgment  which  gives  men  well  to  know  what  is  best 
for  them,  as  well  as  that  faculty  of  invention  which  leads  to  develop- 
ment of  resources  and  to  the  increase  of  wealth  and  comfort,  are  both 
materially  advanced,  perhaps  cannot  rapidly  be  advanced  without,  a 
great  taste  for  pure  speculation  among  the  general  mass  of  the  poople, 
down  to  the  lowest  of  those  who  can  read  and  write.  England  is  a 
marked  example.  Many  persons  will  be  surprised  at  this  assertion. 
They  imagine  that  our  country  is  the  great  instance  of  the  refusal  of 
all  unpractical  knowledge  in  favour  of  what  is  useful.  I  affirm,  on  the 
contrary,  that  there  is  no  country  in  Europe  in  which  there  has  been 
so  wide  a  diffusion  of  speculation,  theory,  or  what  other  unpractical 
word  the  reader  pleases.  In  our  country,  the  scientific  society  is 
always  formed  and  maintained  by  the  people ;  in  every  other,  the 
scientific  academy — most  aptly  named — has  been  the  creation  of  the 
government,  of  which  it  has  never  ceased  to  be  the  nursling.  In  all 
the  parts  of  England  in  which,  manufacturing  pursuits  have  given  the 
artisan  some  command  of  time,  the  cultivation  of  mathematics  and 
other  speculative  studies  has  been,  as  is  well  known,  a  very  frequent 
occupation.  In  no  other  country  has  the  weaver  at  his  loom  bent  over 
the  Principia  of  Newton  ;  in  no  other  country  has  the  man,  of  weekly 
wages  maintained  his  own  scientific  periodical.  With,  us,  since  the 
beginning  of  the  last  century,  scores  upon  scores — perhaps  hundreds, 
for  I  am  far  from  knowing  all — of  annuals  have  run,  some  their  ten 
years,  some  their  half-century,  some  their  century  and  a  half,  con- 
taining questions  to  be  answered,  from  which  many  of  our  examiners 
in  the  Universities  have  culled  materials  for  the  academical  contests. 
And  these  questions  have  always  been  answered,  and  in  cases  without 
number  by  the  lower  order  of  purchasers,  the  mechanics,  the  weavers, 
and  the  printers'  workmen.  I  cannot  here  digress  to  point  out  the 
manner  in  which  the  concentration  of  manufactures,  and  the  general 
diffusion  of  education,  have  affected  the  state  of  things  ;  I  speak  of  the 
time  during  which  the  present  system  took  its  rise,  and  of  the  circum- 
stances under  which  many  of  its  most  effective  promoters  were  trained. 
In  all  this  there  is  nothing  which  stands  out,  like  the  state-nourished 
academy,  with  its  few  great  names  and  brilliant  single  achievements. 
This  country  has  differed  from  all  others  in  the  wide  diffusion  of  tho 
disposition  to  speculate,  which  disposition  has  found  its  place  among 
the  ordinary  habits  of  life,  moderate  in  its  action,  healthy  in  its 
amount.' 


232  A  BUDGET  OF  PARADOXES, 

Among  the  most  remarkable  proofs  of  the  diffusion  of  specu- 
lation was  the  Mathematical  Society,  which  flourished  from  1717 
to  1845.  Its  habitat  was  Spitalfields,  and  I  think  most  of  its 
existence  was  passed  in  Crispin  Street,  It  was  originally  a  plain 
society,  belonging  to  the  studious  artisan.  The  members  met  for 
discussion  once  a  week ;  and  I  believe  I  am  correct  in  saying  that 
each  man  had  his  pipe,  his  pot,  and  his  problem.  One  of  their 
old  rules  was  that,  '  If  any  member  shall  so  far  forget  himself  and 
the  respect  due  to  the  Society  as  in  the  warmth  of  debate  to 
threaten  or  offer  personal  violence  to  any  other  member,  he  shall 
be  liable  to  immediate  expulsion,  or  to  pay  such  fine  as  the 
majority  of  the  members  present  shall  decide.'  But  their  great 
rule,  printed  large  on  the  back  of  the  title  page  of  their  last  book 
of  regulations,  was  '  By  the  constitution  of  the  Society,  it  is  the 
•duty  of  every  member,  if  he  be  asked  any  mathematical  or  philo- 
sophical question  by  another  member,  to  instruct  him  in  the 
plainest  and  easiest  manner  he  is  able.'  We  shall  presently  see 
that,  in  old  time,  the  rule  had  a  more  homely  form. 

I  have  been  told  that  De  Moivre  was  a  member  of  this  Society. 
This  I  cannot  verify :  circumstances  render  it  unlikely ;  even 
though  the  French  refugees  clustered  in  Spitalfields  ;  many  of 
them  were  of  the  Society,  which  there  is  some  reason  to  think 
was  founded  by  them.  But  Dollond,  Thomas  Simpson,  Saun- 
derson,  Crossley,  and  others  of  known  name,  were  certainly 
members.  The  Society  gradually  declined,  and  in  1845  was 
reduced  to  nineteen  members.  An  arrangement  was  made  by 
which  sixteen  of  these-  members,  who  were  not  already  in  the 
Astronomical  Society  became  Fellows  without  contribution,  all 
the  books  and  other  property  of  the  old  Society  being  transferred 
,to  the  new  one.  I  was  one  of  the  committee  which  made  the 
•  preliminary  inquiries,  and  the  reason  of  the  decline  was  soon 
.manifest.  The  only  question  which  could  arise  was  whether  the 
.-members  of  the  society  of  working  men — for  this  repute  still 
continued — were  of  that  class  of  educated  men  who  could  as- 
sociate with  the  Fellows  of  the  Astronomical  Society  on  terms 
agreeable  to  all  parties.  We  found  that  the  artisan  element  had 
been  extinct  for  many  years  ;  there  was  not  a  man  but  might,  as 
to  education,  manners,  and  position,  have  become  a  Fellow  in  the 
usual  way.  The  fact  was  that  life  in  Spitalfields  had  become 
harder  :  and  the  weaver  could  only  live  from  hand  to  mouth,  and 
not  up  to  the  brain.  The  material  of  the  old  Society  no  longer 
existed. 


THE   OLD   MATHEMATICAL   SOCIETY.  233 

In  1798,  experimental  lectures  were  given,  a  small  charge  for 
admission  being  taken  at  the  door  :  by  this  hangs  a  tale — and  a 
song.  Many  years  ago,  I  found  among  papers  of  a  deceased  friend, 
who  certainly  never  had  anything  to  do  with  the  Society,  and 
who  passed  all  his  life  far  from  London,  a  song,  headed  '  Song 
sung  at  a  Mathematical  Society  in  London,  at  a  dinner  given  to 
Mr.  Fletcher,  a  solicitor,  who  had  defended  the  Society  gratis.' 
Mr.  Williams,  the  Assistant  Secretary  of  the  Astronomical  Society, 
formerly  Secretary  of  the  Mathematical  Society,  remembered  that 
the  Society  had  had  a  solicitor  named  Fletcher  among  the 
members.  Some  years  elapsed  before  it  struck  me  that  my  old 
friend  Benjamin  Gompertz,  who  had  long  been  a  member,  might 
have  some  recollection  of  the  matter.  The  folio  wing  is  an  extract 
of  a  letter  from  him  (July  9,  1861) : — 

As  to  the  Mathematical  Society,  of  which  I  was  a  member  when 
only  18  years  of  age,  [Mr.  G.  was  born  in  1779],  having  been,  contrary 
to  the  rules,  elected  under  the  age  of  21.  How  I  came  to  be  a 
member  of  that  Society — and  continued  so  until  it  joined  the  Astro- 
nomical Society,  and  was  then  the  President — was :  I  happened  to 
pass  a  bookseller's  small  shop,  of  second-hand  books,  kept  by  a  poor 
taylor,  but  a  good  mathematician,  John  Griffiths.  I  was  very  pleased 
to  meet  a  mathematician,  and  I  asked  him  if  he  would  give  me  some 
lessons  ;  and  his  reply  was  that  I  was  more  capable  to  teach  him,  but 
he  belonged  to  a  society  of  mathematicians,  and  he  would  introduce 
me.  I  accepted  the  offer,  and  I  was  elected,  and  had  many  scholars 
then  to  teach,  as  one  of  the  rules  was,  if  a  member  asked  for  informa- 
tion, and  applied  to  any  one  who  could  give  it,  he  was  obliged  to  give 
it.,  or  fine  one  penny.  Though  I  might  say  much  with  respect  to  the 
Society  which  would  be  interesting,  I  will  for  the  present  reply  only  to 
your  question.  I  well  knew  Mr.  Fletcher,  who  was  a  very  clever  and 
very  scientific  person.  He  did,  as  solicitor,  defend  an  action  brought 
by  an  informer  against  the  Society — I  think  for  5,OOOZ. — for  giving 
lectures  to  the  public  in  philosophical  subjects  [i.e.  for  unlicensed 
public  exhibition  with  money  taken  at  the  doors].  I  think  the  price 
for  admission  was  one  shilling,  and  we  used  to  have,  if  I  rightly 
recollect,  from  two  to  three  hundred  visitors.  Mr.  Fletcher  was  suc- 
cessful in  his  defence,  and  we  got  out  of  our  trouble.  There  was  a 
collection  made  to  reward  his  services,  but  he  did  not  accept  of  any 
reward  :  and  I  think  we  gave  him  a  dinner,  as  you  state,  and  enjoyed 
ourselves  ;  no  doubt  with  astronomical  songs  and  other  songs  ;  but  my 
recollection  does  not  enable  me  to  say  if  the  astronomical  song  was  a 
drinking  song.  I  think  the  anxiety  caused  by  that  action  was  the 
cause  of  some  of  the  members'  death.  [They  had,  no  doubt,  broken 
the  law  in  ignorance ;  and  by  the  sum  named,  the  informer  must  have 
been  present,  and  sued  for  a  penalty  on  every  shilling  he  could  prove 
to  have  been  taken]. 


234  A  BUDGET  OF  PARADOXES. 

I  by  no  means  guarantee  that  the  whole  song  I  proceed  to  give 
is  what  was  sung  at  the  dinner  :  I  suspect,  by  the  completeness  of 
the  chain,  that  augmentations  have  been  made.  My  deceased 
friend  was  just  the  man  to  add  some  verses,  or  the  addition  may 
have  been  made  before  it  came  into  his  hands,  or  since  his  decease, 
for  the  scraps  containing  the  verses  passed  through  several  hands 
before  they  came  into  mine.  We  may,  however,  be  pretty  sure 
that  the  original  is  substantially  contained  in  what  is  given,  and 
that  the  character  is  therefore  preserved.  I  have  had  myself  to 
repair  damages  every  now  and  then,  in  the  way  of  conjectural 
restoration  of  defects  caused  by  ill-usage. 

THE   ASTRONOMER'S   DRINKING-SONG. 

'  WHOE'ER  would  search  the  starry  sky, 

Its  secrets  to  divine,  sir, 
Should  take  Ms  glass — I  mean,  should  try 

A  glass  or  two  of  wine,  sir  ! 
True  virtue  lies  in  golden  mean, 

And  man  must  wet  his  clay,  sir ; 
Join  these  two  maxims,  and  'tis  seen 

He  should  drink  his  bottle  a  day,  sir  ! 

Old  Archimedes,  reverend  sage  ! 

By  trump  of  fame  renowned,  sir, 
Deep  problems  solved  in  every  page, 

And  the  sphere's  curved  surface  found,  sir: 
Himself  he  would  have  far  outshone, 

And  borne  a  wider  sway,  sir, 
Had  he  our  modern  secret  known, 

And  drank  his  bottle  a  day,  sir ! 

When  Ptolemy,  now  long  ago, 

Believed  the  earth  stood  still,  sir, 
He  never  would  have  blundered  so, 

Had  he  but  drunk  his  fill,  sir : 
He'd  then  have  felt1  it  circulate, 

And  would  have  learnt  to  sav,  sir, 

I/    I  9 

The  true  way  to  investigate 

Is  to  drink  your  bottle  a  day,  sir ! 

Copernicus,  that  learned  wight, 

The  glory  of  his  nation, 
With  draughts  of  wine  refreshed  his  sight, 

And  saw  the  earth's  rotation ; 

1  Dr.  Whewell,  when  I  communicated  this  song  to  him,  started  the  opinion,  which 
I  had  before  him,  that  this  was  a  very  good  idea,  of  which  too  little  was  made. 


THE  ASTRONOMER'S   DRINKING-SONG.  235 

Each  planet  then  its  orb  described, 

The  moon  got  under  way,  sir ; 
T^ese  truths  from  nature  he  imbibed 

For  he  drank  his  bottle  a  day,  sir  ! 

The  noble1  Tycho  placed  the  stars, 

Each  in  its  due  location  ; 
He  lost  his  nose2  by  spite  of  Mars, 

Bnt  that  was  no  privation  : 
Had  he  but  lost  his  mouth,  I  grant 

He  would  have  felt  dismay,  sir, 
Bless  you  !  Tie  knew  what  he  should  want 

To  drink  his  bottle  a  day,  sir  ! 

Cold  water  makes  no  lucky  hits ; 

On  mysteries  the  head  runs  : 
Small  drink  let  Kepler  time  his  wits 

On  the  regular  polyhedrons  : 
He  took  to  wine,  and  it  changed  the  chime, 

His  genius  swept  away,  sir, 
Through  area  varying  3  as  the  time 

At  the  rate  of  a  bottle  a  day,  sir  ! 

Poor  Galileo,  forced  to  rat 

Before  the  Inquisition, 
E  pur  si  muove  was  the  pat 

He  gave  them  in  addition  : 
He  meant,  whate'er  you  think  you  prove, 

The  earth  must  go  its  way,  sirs  ; 
Spite  of  your  teeth  I'll  make  it  move, 

For  I'll  drink  my  bottle  a  day,  sirs  ! 

Great  Newton,  who  was  never  beat 

Whatever  fools  may  think,  sir  ; 
Though  sometimes  he  forgot  to  eat, 

He  never  forgot  to  drink,  sir  : 
Descartes4  took  nought  but  lemonade, 

To  conquer  him  was  play,  sir  ; 
The  first  advance  that  Newton  made 

Was  to  drink  his  bottle  a  day,  sir ! 

1  The  common  epithet  of  rank:  nobilis  Tycho,  as  he  was  a  nobleman.     The  writer 
had  been  at  history. 

2  He   lost   it  in  a  duel,  with  Manderupius  Pasbergius.     A  contemporary,   T.  B. 
Laurus,   insinuates  that  they  fought  to   settle  which  was  the  best  mathematician  ! 
This  seems  odd,  but  it  must  be  remembered  they  fought  in  the  dark,  '  in  tenebris 
densis' ;  and  it  is  a  nice  problem  to  shave  off  a  nose  in  the  dark,  without  any  other 
harm. 

*  Referring  to  Kepler's  celebrated  law  of  planetary  motion.  He  had  previously 
wasted  his  time  on  analogies  between  the  planetary  orbits  and  the  polyhedrons. 

4  As  great  a  lie  as  ever  was  told:  but  in  1800  a  compliment  to  Newton  without  a 
fling  at  Descartes  would  have  been  held  a  lopsided  structure. 


236  A   BUDGET   OF  PARADOXES; 

D'Alemberfc,  Euler,  and  Clairaut, 

Though  they  increased  our  store,  sir, 
Much  further  had  been  seen  to  go 

Had  they  tippled  a  little  more,  sir  ! 
Lagrange  gets  mellow  with  Laplace, 

And  both  are  wont  to  say,  sir, 
The  philosophe  who's  not  an  ass 

Will  drink  his  bottle  a  day,  sir ! 

Astronomers  !    what  can  avail 

Those  who  calumniate  us  ; 
Experiment  can  never  fail 

With  such  an  apparatus  : 
Let  him  who'd  have  his  merits  known 

Remember  what  I  say,  sir ; 
Fair  science  shines  on  him  alone 

Who  drinks  his  bottle  a  day,  sir ! 

How  light  we  reck  of  those  who  mock 

By  this  we'll  make  to  appear,  sir, 
We'll  dine  by  the  sidereal *  clock 

For  one  more  bottle  a  year,  sir  : 
But  choose  which  pendulum  you  will, 

You'll  never  make  your  way,  sir, 
Unless  you  drink — and  drink  your  fill, — 

At  least  a  bottle  a  day,  sir  ! ' 

Old  times  are  changed,  old  manners  gone ! 

There  is  a  new  Mathematical  Society,  and  I  am,  at  this  present 
writing  (1866),  its  first  President.  We  are  very  high  in  the 
newest  developements,  and  bid  fair  to  take  a  place  among  the 
scientific  establishments.  Benjamin  Grompertz,  who  was  President 
of  the  old  Society  when  it  expired,  was  the  link  between  the  old 
and  new  body  :  he  was  a  member  of  ours  at  his  death.  But  not 
a  drop  of  liquor  is  seen  at  our  meetings,  except  a  decanter  of 
water  :  all  our  heavy  is  a  fermentation  of  symbols  ;  and  we  do  not 
draw  it  mild.  There  is  no  penny  fine  for  reticence  or  occult 
science  ;  and  as  to  a  song  !  not  the  ghost  of  a  chance. 

1826.  The  time  may  have  come  when  the  original  documents 
connected  with  the  discovery  of  Neptune  may  be  worth  revising. 
The  following  are  extracts  from  the  Athenceum  of  October  3  and 
October  17  : — 


1  The  sidereal  day  is  about  four  miuutes  short  of  the  solar ;   there  are  366  sidereal 
<3:iys  in  the  year. 


LETTER  FROM  SIR  JOHN  IIERSCIIEL.  237 


LE    VERRIER'S    PLANET. 

"We  have  received,  at  the  last  moment  before  making  up  for 
press,  the  following  letter  from  Sir  John  Herschel,  in  reference 
to  the  matter  referred  to  in  the  communication  from  Mr.  Hind 
given  below  : — 

Collingwood,  Oct.  1. 

'  In  my  address  to  the  British  Association  assembled  at  Southampton, 
on  the  occasion  of  my  resigning  the  chair  to  Sir  R.  Murchison,  I  stated, 
among  the  remarkable  astronomical  events  of  the  last  twelvemonth, 
that  it  had  added  a  new  planet  to  our  list, — adding,  "  it  has  done  more, 
— it  has  given  us  the  probable  prospect  of  the  discovery  of  another. 
We  see  it  as  Columbus  saw  America  from  the  shores  of  Spain.  Its 
movements  have  been  felt,  trembling  along  the  far- reaching  line  of  our 
analysis,  with  a  certainty  hardly  inferior  to  that  of  ocular  demonstra- 
tion."—  These  expressions  are  not  reported  in  any  of  the  papers  which 
profess  to  give  an  account  of  the  proceedings,  but  I  appeal  to  all  pre- 
sent whether  they  were  not  used. 

Give  me  leave  to  state  my  reasons  for  this  confidence ;  and,  in  so 
doing,  to  call  attention  to  some  facts  which  deserve  to  be  put  on  record 
in  the  history  of  this  noble  discovery.  On  July  12,  1842,  the  late 
illustrious  astronomer,  Bessel,  honoured  me  with  a  visit  at  my  present 
residence.  On  the  evening  of  that  day,  conversing  on  the  great  work 
of  the  planetary  reductions  undertaken  by  the  Astronomer  Royal — then 
in  progress,  and  since  published,1 — M.  Bessel  remarked  that  the  mo- 
tions of  Uranus,  as  he  had  satisfied  himself  by  careful  examination  of 
the  recorded  observations,  could  not  be  accounted  for  by  the  pertur- 
bations of  the  known  planets  ;  and  that  the  deviations  far  exceeded  any 
possible  limits  of  error  of  observation.  In  reply  to  the  question, 
Whether  the  deviations  in  question  might  not  be  due  to  the  action 
of  an  unknown  planet  ? — he  stated  that  he  considered  it  highly  pro- 
bable that  such  was  the  case, — being  systematic,  and  such  as  might 
be  produced  by  an  exterior  planet.  I  then  inquired  whether  he  had 
attempted,  from  the  indications  afforded  by  these  perturbations,  to 
discover  the  position  of  the  unknown  body, — in  order  that  "  a  hue  and 
cry  "  might  be  raised  for  it.  From  his  reply,  the  words  of  which  I  do 
not  call  to  mind,  I  collected  that  he  had  not  then  gone  into  that  in- 
quiry ;  but  proposed  to  do  so,  having  now  completed  certain  works 
which  had  occupied  too  much  of  his  time.  And,  accordingly,  in  a 
letter  which  I  received  from  him  after  his  return  to  Konigsberg,  dated 
November  14,  1842,  he  says, — "  In  reference  to  our  conversation  at 
Collingwood,  I  announce  to  you  (melde  ich  Ihnen)  that  Uranus  is  not 
forgotten."  Doubtless,  therefore,  among  his  papers  will  be  found  some 
researches  on  the  subject. 

1  The  expense  of  this  magnificent  work   was  defrayed  by  Government  grants,  ob- 
t  lined,  at  the  instance  of  the  British  Association,  in  1833. 


233  A  BUDGET   OF  PARADOXES. 

The  remarkable  calculations  of  M.  Le  Verrier — which  have  pointed 
oat,  as  now  appears,  nearly  the  true  situation  of  the  new  planet,  by 
resolving  the  inverse  problem  of  the  perturbations — if  uncorroborated 
by  repetition  of  the  numerical  calculations  by  another  hand,  or  by 
independent  investigation  from  another  quarter,  would  hardly  justify 
so  strong  an  assurance  as  that  conveyed  by  my  expressions  above 
alluded  to.  But  it  was  known  to  me,  at  that  time,  (I  will  take  the 
liberty  to  cite  the  Astronomer  Royal  as  my  authority)  that  a  similar 
investigation  had  been  independently  entered  into,  and  a  conclusion  as 
to  the  situation  of  the  new  planet  very  nearly  coincident  with  M.  Le 
Verrier's  arrived  at  (in  entire  ignorance  of  his  conclusions),  by  a  young 
Cambridge  mathematician,  Mr.  Adams  ; — who  will,  I  hope,  pardon  this 
mention  of  his  name  (the  matter  being  one  of  great  historical  moment), 
— and  who  will,  doubtless,  in  his  own  good  time  and  manner,  place  his 
calculations  before  the  public. 

J.  F.  W.  HERSCHEL.' 


Discovery  of  Le  Verrier'' s  Planet. 

Mr.  Hind  announces  to  the  Times  that  be  has  received  a  letter 
from  Dr.  Briinnow,  of  the  Eoyal  Observatory  at  Berlin,  giving  the 
very  important  information  that  Le  Verrier's  planet  was  found  by 
M.  Gralle,  on  the  night  of  September  23.  *  In  announcing  this 
grand  discovery,'  he  says, '  I  think  it  better  to  copy  Dr.  Briinnow's 
letter.' 

Berlin,  Sept.  25. 

'  My  dear  Sir, — M.  Le  Yerrier's  planet  was  discovered  here  the  23rd 
of  September,  by  M.  Galie.  It  is  a  star  of  the  8th  magnitude,  but 
with  a  diameter  of  two  or  three  seconds.  Here  are  its  places  :  — 

h.  m.  s.  R.  A.  Declination. 

Sept.  23,  12    0  14-6  M.T.     328°  19'  16'0"        —13°  24'    8'2" 
Sept.  24,    85440-9M.T.     328°  18'  14-3"        —13°  24' 297" 

The  planet  is  now  retrograde,  its  motion  amounting  daily  to  four 
seconds  of  time. 

Yours  most  respectfully,  BRtTNNOW.' 

'  This  discovery,'  Mr.  Hind  says,  '  may  be  justly  considered  one 
of  the  greatest  triumphs  of  theoretical  Astronomy ; '  and  he  adds, 
in  a  postscript,  that  the  planet  was  observed  at  Mr.  Bishop's 
Observatory,  in  the  Regent's  Park,  on  Wednesday  night,  not- 
withstanding the  moonlight  and  hazy  sky.  '  It  appears  bright,' 
he  says,  '  and  with  a  power  of  320  I  can  see  the  disc.  The 
following  position  is  the  result  of  instrumental  comparisons  with 
33  Aquarii  : — 


THE  DISCOVERY  OF  NEPTUNE.  239 

Sept.  30,  at  8h.  IGm.  21s.  Greenwich  mean  time — 

Right  ascension  of  planet         .         .         21h.  52m.  47'15s. 
South  declination    ,  13°  27'  20".' 


THE   NEW   PLANET. 

Cambridge  Observatory,  Oct.  15. 

The  allusion  made  by  Sir  John  Herschel,  in  his  letter  contained  in 
the  Athenaeum  of  October  3,  to  the  theoretical  researches  of  Mr. 
Adams,  respecting  the  newly-discovered  planet,  has  induced  me  to 
request  that  you  would  make  the  following  communication  public.  It 
is  right  that  I  should  first  say  that  I  have  Mr.  Adams's  permission  to 
make  the  statements  that  follow,  so  far  as  they  relate  to  his  labours. 
I  do  not  propose  to  enter  into  a  detail  of  the  steps  by  which  Mr.  Adams 
was  led,  by  his  spontaneous  and  independent  researches,  to  a  conclusion 
that  a  planet  must  exist  more  distant  than  Uranus.  The  matter  is  of 
too  great  historical  moment  not  to  receive  a  more  formal  record  than 
it  would  be  proper  to  give  it  here.  My  immediate  object  is  to  show, 
while  the  attention  of  the  scientific  public  is  more  particularly  directed 
to  the  subject,  that,  with  respect  to  this  remarkable  discovery,  English 
astronomers  may  lay  claim  to  some  merit. 

Mr.  Adams  formed  the  resolution  of  trying,  by  calculation,  to  account 
for  the  anomalies  in  the  motion  of  Uranus  on  the  hypothesis  of  a  more 
distant  planet,  when  he  was  an  undergraduate  in  this  University,  and 
when  his  exertions  for  the  academical  distinction,  which  he  obtained 
in  January  1843,  left  him  no  time  for  pursuing  the  research.  In  the 
course  of  that  year,  he  arrived  at  an  approximation  to  the  position  of 
the  supposed  planot ;  which,  however,  he  did  not  consider  to  be  worthy 
of  confidence,  on  account  of  his  not  having  employed  a  sufficient  number 
of  observations  of  Uranus.  Accordingly,  he  requested  my  intervention 
to  obtain  for  him  the  early  Greenwich  observations,  then  in  course  of 
reduction ; — which  the  Astronomer  Royal  immediately  supplied,  in  the 
kindest  possible  manner.  This  was  in  February,  1844.  In  September, 
1845,  Mr.  Adams  communicated  to  me  values  which  he  had  obtained 
for  the  heliocentric  longitude,  excentricity  of  orbit,  longitude  of  peri- 
helion, and  mass,  of  an  assumed  exterior  planet, — deduced  entirely 
from  unaccounted-for  perturbations  of  Uranus.  The  same  results, 
somewhat  corrected,  he  communicated,  in  October,  to  the  Astronomer 
Royal.  M.  Le  Verrier,  in  an  investigation  which  was  published  in 
June  of  184(5,  assigned  very  nearly  the  same  heliocentric  longitude  for 
the  probable  position  of  the  planet  as  Mr.  Adams  had  arrived  at,  but 
gave  no  results  respecting  its  mass  and  the  form  of  its  orbit.  The 
coincidence  as  to  position  from  two  entirely  independent  investigations 
naturally  inspired  confidence ;  and  the  Astronomer  Royal  shortly  after 
suggested  the  employing  of  the  Northumberland  telescope  of  this 
Observatory  in  a  systematic  search  after  the  hypothetical  planet ;  re- 
commending, at  the  same  time,  a  definite  plan  of  operations.  I  under- 


240 


A  BUDGET   OF  PARADOXES. 


took  to  make  the  search,  —  and  commenced  observing  on  July  29; 
The  observations  were  directed,  in  the  first  instance,  to  the  part  of  the 
heavens  which  theory  had  pointed  out  as  -the  most  probable  place  of 
the  planet  ;  in  selecting  which  I  was  guided  by  a  paper  drawn  up  for 
me  by  Mr.  Adams.  Not  having  hour  xxi.  of  the  Berlin  star-maps  —  of 
the  publication  of  which  I  was  not  aware  —  I  had  to  proceed  on  the 
principle  of  comparison  of  observations  made  at  intervals.  On  July  30, 
I  went  over  a  zone  9'  broad,  in  such  a  manner  as  to  include  all  stars 
to  the  eleventh  magnitude.  On  August  4,  I  took  a  broader  zone,  — 
and  recorded  a  place  of  the  planet.  My  next  observations  were  on 
August  12  ;  when  I  met  with  a  star  of  the  eighth  magnitude  in  the 
zone  which  T  had  gone  over  on  July  30,  —  and  which  did  not  then 
contain  this  star.  Of  course,  this  was  the  planet  ;  —  the  place  of  which 
was,  thus,  recorded  a  second  time  in  four  days  of  observing.  A  com- 
parison of  the  observations  of  July  30  and  August  12  would,  according 
to  the  principle  of  search  which  I  employed,  have  shown  me  the  planet. 
I  did  not  make  the  comparison  till  after  the  detection  of  it  at  Berlin  — 
partly  because  I  had  an  impression  that  a  much  more  extensive  search 
was  required  to  give  any  probability  of  discovery  —  and  partly  from  the 
press  of  other  occupation.  The  planet,  however,  was  secured,  and  two 
positions  of  it  recorded  six  weeks  earlier  here  than  in  any  other 
observatory,  —  and  in  a  systematic  search  expressly  undertaken  for  that 
purpose.  I  give  now  the  positions  of  the  planet  on  August  4  and 
August  12. 


Greenwich  mean  time. 

m    2<5s 
6m.  25s. 

-?m    2fi« 
3m.  26s. 


AIID-    4 
Aug.    4, 

Am*   12 
Aug.  12, 


/R.A.         21h.  58m.  14'70s. 
^NPD      102°  57'      32'2" 

R'A'         21h.  57m.  26'13s. 
103o  2,        fl.2« 


From  these  places  compared  with  recent  observations  Mr.  Adams 
has  obtained  the  following  results  :  — 


Distance  of  the  planet  from  the  sun 
Inclination  of  the  orbit    .         .         . 
Longitude  of  the  descending  node 
Heliocentric  longitude,  Aug.  4 


30-05 
1°  45' 
309°  43' 
326°  39' 


The  present  distance  from  the  sun  is,  therefore,  thirty  times  the  earth's 
mean  distance  ;  —  which  is  somewhat  less  than  the  theory  had  indicated. 
The  other  elements  of  the  orbit  cannot  be  approximated  to  till  the 
observations  shall  have  been  continued  for  a  longer  period. 

The  part  taken  by  Mr.  Adams  in  the  theoretical  search  after  this 
planet  will,  perhaps,  be  considered  to  justify  the  suggesting  of  a  name.. 
With  his  consent,  I  mention  Oceanus  as  one  which  may  possibly  receive 
the  votes  of  astronomers.  —  I  have  authority  to  state  that  Mr.  Adams's 
investigations  will,  in  a  short  time,  be  published  in  detail. 

J.  CHALLIS.' 


DISCOVERY   OF  NEPTUNE  241 


ASTRONOMICAL  POLICE   REPORT. 

"  An  ill-looking  kind  of  body,  who  declined  to  give  any  name, 
was  brought  before  the  Academy  of  Sciences,  charged  with  having 
assaulted  a  gentleman  of  the  name  of  Uranus  in  the  public 
highway.  The  prosecutor  was  a  youngish  looking  person,  wrapped 
up  in  two  or  three  great  coats ;  and  looked  chillier  than  any- 
thing imaginable,  except  the  prisoner, — whose  teeth  absolutely 
shook,  all  the  time. 

Policeman  Le  Verrier  stated  that  he  saw  the  prosecutor  walking 
along  the  pavement,  —  and  sometimes  turning  sideways,  and 
sometimes  running  up  to  the  railings  and  jerking  about  in  a 
strange  way.  Calculated  that  somebody  must  be  pulling  his 
coat,  or  otherwise  assaulting  him.  It  was  so  dark  that  he  could 
not  see ;  but  thought,  if  he  watched  the  direction  in  which  the 
next  odd  move  was  made,  he  might  find  out  something.  When 
the  time  came,  he  set  Briinnow,  a  constable  in  another  division 
of  the  same  force,  to  watch  where  he  told  him ;  and  Briinnow 
caught  the  prisoner  lurking  about  in  the  very  spot, — trying  to 
look  as  if  he  was  minding  his  own  business.  Had  suspected  for 
a  long  time  that  somebody  was  lurking  about  in  the  neighbour- 
hood. Briinnow  was  then  called,  and  deposed  to  his  catching  the 
prisoner  as  described. 

M.  Arago. — Was  the  prosecutor  sober  ? 

Le  Verrier. — Lord,  yes,  your  worship  ;  no  man  who  had  a  drop 
in  him  ever  looks  so  cold  as  he  did. 

M.  Arago. — Did  you  see  the  assault  ? 

Le  Verrier. — I  can't  say  I  did ;  but  I  told  Briinnow  exactly 
how  he'd  be  crouched  down, — just  as  he  was. 

M.  Arago  (to  Briinnow}. — Did  you  see  the  assault  ? 

Briinnow. — No,  your  worship  ;  but  I  caught  the  prisoner. 

M.  Arago. — How  do  you  know  there  was  any  assault  at  all  ? 

Le  Verrier. — I  reckoned  it  could'nt  be  otherwise,  when  I  saw 
the  prosecutor  making  those  odd  turns  on  the  pavement. 

M.  Arago. — You  reckon  and  you  calculate  I  Why,  you'll  tell 
me,  next,  that  you  policemen  may  sit  at  home  and  find  out  all 
that's  going  on  in  the  streets  by  arithmetic.  Did  you  ever  bring 
a  case  of  this  kind  before  me  till  now  ? 

Le  Verriar. — Why,  you  see,  your  worship,  the  police  are  grow- 
ing cleverer  and  cleverer  every  day.  We  can't  help  it : — it  grows 
upon  us. 

fc 


242  A    BUDGET   OF  PAKADOXES. 

M.  Arago. — You're  getting  too  clever  for  me.  What  does  the 
prosecutor  know  about  the  matter  ? 

The  prosecutor  said,  all  he  knew  was  that  he  was  pulled  behind 
by  somebody  several  times.  On  being  further  examined,  he  said 
that  he  had  seen  the  prisoner  often,  but  did  not  know  his  name, 
nor  how  he  got  his  living;  but  had  understood  he  was  called 
Neptune.  He  himself  had  paid  rates  and  taxes  a  good  many 
years  now.  Had  a  family  of  six, — two  of  whom  got  their  own 
living. 

The  prisoner,  being  called  on  for  his  defence,  said  that  it  was 
a  quarrel.  He  had  pushed  the  prosecutor — and  the  prosecutor 
had  pushed  him.  They  had  known  each  other  a  long  time,  and 
were  always  quarrelling ; — he  did  not  know  why.  It  was  their 
nature,  he  supposed.  He  further  said,  that  the  prosecutor  had 
given  a  false  account  of  himself; — that  he  went  about  under 
different  names.  Sometimes  he  was  called  Uranus,  sometimes 
Herschel,  and  sometimes  Greorgium  Sidus;  and  he  had  no 
character  for  regularity  in  the  neighbourhood.  Indeed,  he  was 
sometimes  not  to  be  seen  for  a  long  time  at  once. 

The  prosecutor,  on  being  asked,  admitted,  after  a  little  hesita- 
tion, that  he  had  pushed  and  pulled  the  prisoner  too.  In  the 
altercation  which  followed,  it  was  found  very  difficult  to  make 
out  which  began  : — and  the  worthy  magistrate  seemed  to  think 
they  must  have  begun  together. 

M.  Arago. — Prisoner,  have  you  any  family  ? 

The  prisoner  declined  answering  that  question  at  present.  He 
said  he  thought  the  police  might  as  well  reckon  it  out  whether 
he  had  or  not. 

M.  Arago  said  he  didn't  much  differ  from  that  opinion. — He 
Jien  addressed  both  prosecutor  and  prisoner ;  and  told  them  that 
if  they  couldn't  settle  their  differences  without  quarrelling  in 
the  streets,  he  should  certainly  commit  them  both  next  time. 
In  the  meantime,  he  called  upon  both  to  enter  into  their  own 
recognizances ;  and  directed  the  police  to  have  an  eye  upon  both, 
— observing  that  the  prisoner  would  be  likely  to  want  it  a  long 
time,  and  the  prosecutor  would  be  not  a  hair  the  worse  for  it." 

This  squib  was  written  by  a  person  who  was  among  the  astrono- 
mers :  and  it  illustrates  the  fact  that  Le  Verrier  had  sole  posses- 
sion of  the  field  until  Mr.  Challis's  letter  appeared.  Sir  John 
Herschel's  previous  communication  should  have  paved  the  way  : 
but  the  wonder  of  the  discovery  drove  it  out  of  many  heads. 
There  is  an  excellent  account  of  the  whole  matter  in  Professor 


THE  MOON  AND  THE   TIDES.  243 

Grant's  '  History  of  Physical  Astronomy.'  The  squib  scandalized 
some  grave  people,  who  wrote  severe  admonitions  to  the  editor. 
There  are  formalists  who  spend  much  time  in  writing  propriety 
to  journals,  to  which  they  serve  as  foolometers.  In  a  letter  to 
the  Athenceum,  speaking  of  the  way  in  which  people  hawk  fine 
terms  for  common  things,  I  said  that  these  people  ought  to  have 
a  new  translation  of  the  Bible,  which  should  contain  the  verse 
*  gentleman  and  lady,  created  He  them.'  The  editor  was  hand- 
somely fired  and  brimstoned ! 

A  new  theory  of  the  tides  :  in  which  the  errors  of  the  usual  theory 
are  demonstrated  ;  and  proof  shewn  that  the  full  moon  is  not 
the  cause  of  a  concomitant  spring  tide,  but  actually  the  cause  of 
the  neaps  .  .  .  By  Commr.  Debenham,  B.N.  London,  1846, 
8vo. 

The  author  replied  to  a  criticism  in  the  Athenceum,  and  I 
remember  how,  in  a  very  few  words,  he  showed  that  he  had 
read  nothing  on  the  subject.  The  reviewer  spoke  of  the  forces  of 
the  planets  (i.e.  the  Sun  and  Moon)  on  the  Ocean,  on  which  the 
author  remarks,  '  But  N.B.  the  Sun  is  no  planet,  Mr.  Critic.' 
Had  he  read  any  of  the  actual  investigations  on  the  usual  theory, 
he  would  have  known  that  to  this  day  the  sun  and  moon  con- 
tinue to  be  called  planets — though  the  phrase  is  disappearing — 
in  speaking  of  the  tides ;  the  sense,  of  course,  being  the  old  one, 
wandering  bodies. 

A  large  class  of  the  paradoxers,  when  they  meet  with  some- 
thing which  taken  in  their  sense  is  absurd,  do  not  take  the 
trouble  to  find  out  the  intended  meaning,  but  walk  off  with  the 
words  laden  with  their  own  first  construction.  Such  men  are 
hardly  fit  to  walk  the  streets  without  an  interpreter.  I  was 
startled  for  a  moment,  at  the  time  when  a  recent  happy — and 
more  recently  happier — marriage  occupied  the  public  thoughts, 
by  seeing  in  a  haberdasher's  window,  in  staring  large  letters,  an 
unpunctuated  sentence  which  read  itself  to  me  as  '  Princess 
Alexandra!  collar  and  cuff!'  It  immediately  occurred  to  me 
that  had  I  been  any  one  of  some  scores  out  of  my  paradoxers, 
I  should,  no  doubt,  have  proceeded  to  raise  the  mob  against 
the  unscrupulous  person  who  dared  to  hint  to  a  young  bride  such 
maleficent — or  at  least  immellificent — conduct  towards  her  new 
lord.  But,  as  it  was,  certain  material  contexts  in  the  shop 
window  suggested  a  less  savage  explanation.  A  paradoxer  should 
not  stop  at  reading  the  advertisements  of  Newton  or  Laplace  :  he 
should  learn  to  look  at  the  stock  of  goods. 


244  A  BUDGET   OF  PAEADOXES. 

I  think  I  must  have  an  eye  for  double  readings,  when  pre- 
sented :  though  I  never  guess  riddles.  On  the  day  on  which  I 
first  walked  into  the  Panizzi  reading  room — as  it  ought  to  be 
called — at  the  Museum,  I  began  my  circuit  of  the  wall-shelves 
at  the  ladies'  end :  and  perfectly  coincided  in  the  propriety  of 
the  Bibles  and  theological  works  being  placed  there.  But  the 
very  first  book  I  looked  on  the  back  of  had,  in  flaming  gold 
letters,  the  following  inscription — '  Blast  the  Antinomians  ! '  If 
a  line  had  been  drawn  below  the  first  word,  Dr.  Blast's  history 
of  the  Antinomians  would  not  have  been  so  fearfully  misinter- 
preted. It  seems  that  neither  the  binder  nor  the  arranger  of  the 
room  had  caught  my  reading.  The  book  was  removed  before  the 
catalogue  of  books  of  reference  was  printed. 

Two  systems  of  astronomy  :  first,  the  Newtonian  system,  showing 
the  rise  and  progress  thereof,  with  a  short  historical  account ; 
the  general  theory  with  a  variety  of  remarks  thereon :  second, 
the  system  in  accordance  with,  the  Holy  Scriptures,  showing 
the  rise  and  progress  from  Enoch,  the  seventh  from  Adam,  the 
prophets,  Moses,  and  others,  in  the  first  Testament ;  our  Lord 
Jesus  Christ,  and  his  apostles,  in  the  new  or  second  Testament ; 
Reeve  and  Muggleton,  in  the  third  and  last  Testament ;  with 
a  variety  of  remarks  thereon.  By  Isaac  Frost.  London,  1846, 
4to. 

A  very  handsomely  printed  volume,  with  beautiful  plates. 
Many  readers  who  have  heard  of  Muggleton ians  have  never  had 
any  distinct  idea  of  Lodowick  Muggleton,  the  inspired  tailor, 
(1608-1698)  who  about  1650  received  his  commission  from 
heaven,  wrote  a  Testament,  founded  a  sect,  and  descended  to 
posterity.  Of  Eeeve  less  is  usually  said  ;  according  to  Mr.  Frost, 
he  and  Muggleton  are  the  two  'witnesses.'  I  shall  content 
myself  with  one  specimen  of  Mr.  Frost's  science : 

"  I  was  once  invited  to  hear  read  over  '  Guthrie  on  Astronomy,'  and 
when  the  reading  was  concluded  I  was  asked  my  opinion  thereon  ; 
when  I  said,  '  Doctor,  it  appears  to  me  that  Sir  I.  Newton  has  only 
given  two  proofs  in  support  of  his  theory  of  the  earth  revolving  round 
the  sun :  all  the  rest  is  assertion  without  any  proofs.' — '  What  are 
they  ? '  inquired  the  Doctor. — '  Well,'  I  said,  '  they  are,  first,  the 
power  of  attraction  to  keep  the  earth  to  the  sun ;  the  second  is  the 
power  of  repulsion,  by  virtue  of  the  centrifugal  motion  of  the  earth  : 
all  the  rest  appears  to  me  assertion  without  proof.'  The  Doctor  con- 
sidered a  short  time,  and  then  said,  '  It  certainly  did  appear  so.'  I 
said,  '  Sir  Isaac  has  certainly  obtained  the  credit  of  completing  the 
system,  but  really  he  has  only  half  done  his  work.' — '  How  is  that,' 


MUGGLETON — GEORGE  FOX.  245 

inquired  my  friend  the  Doctor.  My  reply  was  this:  'You  -will 
observe  his  system  shows  the  earth  traverses  round  the  sun  on  an 
inclined  plane  ;  the  consequence  is,  there  are  four  powers  required  to 
make  his  system  complete  : 

1st.     The  power  of  attraction. 

2ndly.     The  power  of  repulsion. 

3rdly.     The  power  of  ascending  the  inclined  plane. 

4thly.     The  power  of  descending  the  inclined  plane. 

You  will  thus  easily  see  the  four  powers  required,  and  Newton  has 
only  accounted  for  two ;  the  work  is  therefore  only  half  done.'  Upon 
due  reflection  the  Doctor  said,  '  It  certainly  was  necessary  to  have 
these  four  points  cleared  up  before  the  system  could  be  said  to  be 
complete.'  ' 

I  have  no  doubt  that  Mr.  Frost,  and  many  others  on  ray  list, 
have  really  encountered  doctors  who  could  be  puzzled  by  such 
stuff  as  this,  or  nearly  as  bad,  among  the  votaries  of  existing 
systems,  and  have  been  encouraged  thereby  to  print  their  ob- 
jections. But  justice  requires  me  to  say  that  from  the  words 
'  power  of  repulsion  by  virtue  of  the  centrifugal  motion  of  the 
earth,'  Mr.  Frost  may  be  suspected  of  having  something  more 
like  a  notion  of  the  much-mistaken  term  '  centrifugal  force ' 
than  many  paradoxers  of  greater  fame.  The  Muggletonian  sect 
is  not  altogether  friendless :  over  and  above  this  handsome 
volume,  the  works  of  Eeeve  and  Muggleton  were  printed,  in  1832, 
in  three  quarto  volumes.  See  Notes  and  Queries,  1st  Series,  v. 
80  ;  3rd  Series,  iii,  303. 

[The  system  laid  down  by  Mr.  Frost,  though  intended  to  be 
substantially  that  of  Lodowick  Muggleton,  is  not  so  vagari- 
ous. It  is  worthy  of  note  how  very  different  have  been  the 
fates  of  two  contemporary  paradoxers,  Muggleton  and  George 
Fox.  They  were  friends  and  associates,  and  commenced  their 
careers  about  the  same  time,  1647-1650.  The  followers  of  Fox 
have  made  their  sect  an  institution,  and  deserve  to  be  called 
the  pioneers  of  philanthropy.  But  though  there  must  still  be 
Muggletonian s,  since  expensive  books  are  published  by  men  who 
take  the  name,  no  sect  of  that  name  is  known  to  the  world. 
Nevertheless,  Fox  and  Muggleton  are  men  of  one  type,  developed 
by  the  same  circumstances  :  it  is  for  those  who  investigate  such 
men  to  point  out  why  their  teachings  have  had  fates  so  different. 
Macaulay  says  it  was  because  Fox  found  followers  of  more  sense 
than  himself.  True  enough :  but  why  did  Fox  find  such 
followers  and  not  Muggleton  ?  The  two  were  equally  crazy,  to 


246  A  BUDGET   OF  PARADOXES. 

all  appearance :  and  the  difference  required  must  be  sought  in 
the  doctrines  themselves. 

Fox  was  not  a  rational  man  :  but  the  success  of  his  sect  and 
doctrines  entitles  him  to  a  letter  of  alteration  of  the  phrase 
which  I  am  surprised  has  not  become  current.  When  Conduitt, 
the  husband  of  Newton's  half-niece,  wrote  a  circular  to  Newton's 
friends,  just  after  his  death,  inviting  them  to  bear  their  parts  in 
a  proper  biography,  he  said,  '  As  Sir  I.  Newton  was  a  national 
man,  I  think  every  one  ought  to  contribute  to  a  work  intended 
to  do  him  justice.'  Here  is  the  very  phrase  which  is  often 
wanted  to  signify  that  celebrity  which  puts  its  mark,  good  or 
bad,  on  the  national  history,  in  a  manner  which  cannot  be 
asserted  of  many  notorious  or  famous  historical  characters.  Thus 
George  Fox  and  Newton  are  both  national  men.  Dr.  Eoget's 
Thesaurus  gives  more  than  fifty  synonyms — colleagues  would  be 
the  better  word — of  *  celebrated,'  any  one  of  which  might  be 
applied,  either  in  prose  or  poetry,  to  Newton  or  to  his  works,  no 
one  of  which  comes  near  to  the  meaning  which  Conduitt's  ad- 
jective immediately  suggests. 

The  truth  is,  that  we  are  too  monarchical  to  be  national. 
We  have  the  Queen's  army,  the  Queen's  navy,  the  Queen's  high- 
way, the  Queen's  English,  &c. ;  nothing  is  national  except  the 
debt.  That  this  remark  is  not  new  is  an  addition  to  its  force ; 
it  has  hardly  been  repeated  since  it  was  first  made.  It  is  some 
excuse  that  nation  is  not  vernacular  English  :  the  country  is  our 
word,  and  country  man  is  appropriated.] 

Astronomical  Aphorisms,  or  Theory  of  Nature ;  founded  on  the 
immutable  basis  of  Meteoric  Action.  By  P.  Murphy,  Esq. 
London,  1847,  12mo. 

This  is  by  the  framer  of  the  Weather  Almanac,  who  appeals  to 
that  work  as  corroborative  of  his  theory  of  planetary  temperature, 
years  after  all  the  world  knew  by  experience  that  this  meteorolo- 
gical theory  was  just  as  good  as  the  others. 

The  conspiracy  of  the  Bullionists  as  it  affects  the  present  system 
of  the  money  laws.  By  Caleb  Quotem.  Birmingham,  1847, 
8vo.  (pp.  16). 

This  pamphlet  is  one  of  a  class  of  which  I  know  very  little, 
in  which  the  effects  of  the  laws  relating  to  this  or  that  political 
bone  of  contention  are  imputed  to  deliberate  conspiracy  of  one 
class  to  rob  another  of  what  the  one  knew  ought  to  belong  to  the 


THEISM   INDEPENDENT   OF   REVELATION.  247 

other.  The  success  of  such  writers  in  believing  what  they  have 
a  bias  to  believe,  would,  if  they  knew  themselves,  make  them 
think  it  equally  likely  that  the  inculpated  classes  might  really 
believe  what  it  is  their  interest  to  believe.  The  idea  of  a  guilty 
understanding  existing  among  fundholders,  or  landholders,  or 
any  holders,  all  the  country  over,  and  never  detected  except  by 
bouncing  pamphleteers,  is  a  theory  which  should  have  been  left 
for  Cobbett  to  propose,  and  for  Apella  to  believe. 

[August,  1866.  A  pamphlet  shows  how  to  pay  the  National 
Debt.  Advance  paper  to  railways,  &c.,  receivable  in  payment  of 
taxes.  The  railways  pay  interest  and  principal  in  money,  with 
which  you  pay  your  national  debt,  and  redeem  your  notes. 
Twenty-five  years  of  interest  redeems  the  notes,  and  then  the 
principal  pays  the  debt.  Notes  to  be  kept  up  to  value  by  penal- 
ties.] 

The  Reasoner.     No.  45.     Edited  by  G.  J.  Holyoake.     Price  "2d. 
Is  there  sufficient  proof  of  the  existence  of  God  ?     8vo.    1847. 

This  acorn  of  the  holy  oak  was  forwarded  to  me  with  a  manu- 
script note,  signed  by  the  editor,  on  the  part  of  the  '  London 
Society  of  Theological  Utilitarians,'  who  say  '  they  trust  you 
may  be  induced  to  give  this  momentous  subject  your  considera- 
tion.' The  supposition  that  a  middle-aged  person,  known  as  a 
student  of  thought  on  more  subjects  than  one,  had  that  particular 
subject  yet  to  begin,  is  a  specimen  of  what  I  will  call  the  as- 
sumption-trick of  controversy,  a  habit  which  pervades  all  sides 
of  all  subjects.  The  tract  is  a  proof  of  the  good  policy  of  letting 
opinions  find  their  level,  without  any  assistance  from  the  Court 
of  Queen's  Bench.  Twenty  years  earlier  the  thesis  would  have 
been  positive,  '  There  is  sufficient  proof  of  the  non-existence  of 
God,'  and  bitter  in  its  tone.  As  it  stands,  we  have  a  moderate 
and  respectful  treatment — wrong  only  in  making  the  opponent 
argue  absurdly,  as  usually  happens  when  one  side  invents  the 
other — of  a  question  in  which  a  great  many  Christians  have 
agreed  with  the  atheist :  that  question  being — Can  the  existence 
of  God  be  proved  independently  of  revelation?  Many  very 
religious  persons  answer  this  question  in  the  negative,  as  well 
as  Mr.  Holyoake.  And,  this  point  being  settled,  all  who  agree 
in  the  negative  separate  into  those  who  can  endure  scepticism, 
and  those  who  cannot :  the  second  class  find  their  way  to  Chris- 
tianity. This  very  number  of  '  The  Reasoner '  announces  the 
secession  of  one  of  its  correspondents,  and  his  adoption  of  the 
Christian  faith.  This  would  not  have  happened  twenty  years 


248  A  BUDGET  OF  PARADOXES. 

before :  nor,  had  it  happened,  would  it  have  been  respectfully 
announced. 

There  are  people  who  are  very  unfortunate  in  the  expres- 
sion of  their  meaning.  Mr.  Holyoake,  in  the  name  of  the 
4  London  Society,'  &c.,  forwarded  a  pamphlet  on  the  existence 
of  Grod,  and  said  that  the  Society  trusted  I  '  may  be  induced  to 
give '  the  subject  my  '  consideration.'  How  could  I  know  the 
Society  was  one  person,  who  supposed  I  had  arrived  at  a  conclu- 
sion, and  wanted  a  *  guiding  word '  ?  But  so  it  seems  it  was  : 
Mr.  Holyoake,  in  the  English  Leader  of  October  15,  1864,  and  in 
a  private  letter  to  me,  writes  as  follows : — 

"  The  gentleman  who  was  the  author  of  the  argument,  and  who  asked 
me  to  send  it  to  Mr.  De  Morgan,  never  assumed  that  that  gentleman 
had  '  that  particular  subject  to  begin  ' — on  the  contrary,  he  supposed 
that  one  whom  we  all  knew  to  be  eminent  as  a  thinker  had  come  to  a 
conclusion  upon  it,  and  would  perhaps  vouchsafe  a  guiding  word  to 
one  who  was,  as  yet,  seeking  the  solution  of  the  Great  Problem  of 
Theology.  I  told  my  friend  that  '  Mr.  De  Morgan  was  doubtless  pre- 
occupied, and  that  he  must  be  content  to  wait.  On  some  day  of 
courtesy  and  leisure  he  might  have  the  kindness  to  write.'  Nor  was 
I  wrong — the  answer  appears  in  your  pages  at  the  lapse  of  seventeen 
years." 

I  suppose  Mr.  Holyoake's  way  of  putting  his  request  was  the 
stylus  curice  of  the  Society.  A  worthy  Quaker  who  was  sued 
for  debt  in  the  King's  Bench  was  horrified  to  find  himself 
charged  in  the  declaration  with  detaining  his  creditor's  money 
by  force  and  arms,  contrary  to  the  peace  of  our  Lord  the  King, 
&c.  It's  only  the  stylus  curice,  said  a  friend:  I  don't  know 
curice,  said  the  Quaker,  but  he  shouldn't  style  us  peace-breakers. 
The  notion  that  the  nori-existence  of  Grod  can  be  proved,  has 
died  out  under  the  light  of  discussion :  had  the  only  lights 
shone  from  the  pulpit  and  the  prison,  so  great  a  step  would  never 
have  been  made.  The  question  now  is  as  above.  The  dictum 
that  Christianity  is  '  part  and  parcel  of  the  law  of  the  land '  is 
also  abrogated  :  at  the  same  time,  and  the  coincidence  is  not 
an  accident,  it  is  becoming  somewhat  nearer  the  truth  that  the 
law  of  the  land  is  part  and  parcel  of  Christianity.  It  must  also 
be  noticed  that  Christianity  was  part  and  parcel  of  the  articles 
of  war;  and  so  was  duelling.  Any  officer  speaking  against 
religion  was  to  be  cashiered  ;  and  any  officer  receiving  an  affront 
without,  in  the  last  resort,  attempting  to  kill  his  opponent,  was 
also  to  be  cashiered.  Though  somewhat  of  a  book-hunter,  I 
have  never  been  able  to  ascertain  the  date  of  the  collected 


LOST  EPISCOPAL  PBOTEST.  249 

remonstrances  of  the  prelates  in  the  House  of  Lords  against  this 
overt  inculcation  of  murder,  under  the  soft  name  of  satisfaction  : 
it  is  neither  in  Watt,  nor  in  Lowndes,  nor  in  any  edition  of 
Brunet ;  and  there  is  no  copy  in  the  British  Museum.  Was  the 
collected  edition  really  published  ? 

[The  publication  of  the  above  in  the  Athenceum  has  not  pro- 
duced reference  to  a  single  copy.  The  collected  edition  seems 
to  be  doubted.  I  have  even  met  one  or  two  persons  who  doubt 
the  fact  of  the  Bishops  having  remonstrated  at  all :  but  their 
doubt  was  founded  on  an  absurd  supposition,  namely,  that  it  was 
no  business  of  theirs  ;  that  it  was  not  the  business  of  the  prelates 
of  the  Church  in  union  with  the  State  to  remonstrate  against 

O 

the  Crown  commanding  murder !  Some  say  that  the  edition 
was  published,  but  under  an  irrelevant  title,  which  prevented 
people  from  knowing  what  it  was  about.  Such  things  have 
happened :  for  example,  arranged  extracts  from  Wellington's 
general  orders,  which  would  have  attracted  attention,  fell 
dead  under  the  title  of  'Principles  of  War.'  It  is  surmised 
that  the  book  I  am  looking  for  also  contains  the  protests  of 
the  Eeverend  bench  against  other  things  besides  the  Thou-shalt- 
do-murder  of  the  Articles  (of  war),  and  is  called  *  First  Elements 
of  Eeligion '  or  some  similar  title.  Time  clears  up  all  things.] 

With  the  general  run  of  the  philosophical  atheists  of  the  last 
century  the  notion  of  a  God  was  an  hypothesis.  There  was  left 
an  admitted  possibility  that  the  vague  somewhat  which  went  by 
more  names  than  one,  might  be  personal,  intelligent,  and  super- 
intendent. In  the  works  of  Laplace,  who  is  sometimes  called 
an  atheist  from  his  writings,  there  is  nothing  from  which  such 
an  inference  can  be  drawn  :  unless  indeed  a  Eeverend  Fellow  of 
the  Eoyal  Society  may  be  held  to  be  the  fool  who  said  in  his 
heart,  &c.  &c.,  if  his  contributions  to  the  Philosophical  Trans- 
actions go  no  higher  than  nature.  The  following  anecdote  is 
well  known  in  Paris,  but  has  never  been  printed  entire.  Laplace 
once  went  in  form  to  present  some  edition  of  his  { Systeme  dti 
Monde '  to  the  First  Consul,  or  Emperor.  Napoleon,  whom  some 
wags  had  told  that  this  book  contained  no  mention  of  the  name 
of  God,  and  who  was  fond  of  putting  embarrassing  questions, 
received  it  with — '  M.  Laplace,  they  tell  me  you  have  written 
this  large  book  on  the  system  of  the  universe,  and  have  never 
even  mentioned  its  Creator.'  Laplace,  who,  though  the  most 
supple  of  politicians,  was  as  stiff  as  a  martyr  on  every  point  of 


250  A  BUDGET  OF  PARADOXES. 

his  philosophy  or  religion  (ex.  gr.  even  under  Charles  X.  he 
never  concealed  his  dislike  of  the  priests),  drew  himself  up,  and 
answered  bluntly,  '  Je  n'avais  pas  hesoin  de  cette  hypothese-la.' 
Napoleon,  greatly  amused,  told  this  reply  to  Lagrange,  who 
exclaimed,  '  Ah  I  c'est  une  belle  hypothese ;  ca  explique  beaucoup 
de  choses.' 

It  is  commonly  said  that  the  last  words  of  Laplace  were  '  Ce 
que  nous  connaissons  est  peu  de  chose ;  ce  que  nous  ignorons 
est  immense.'  This  looks  like  a  parody  on  Newton's  pebbles  : 
the  following  is  the  true  account ;  it  comes  to  me  through  one 
remove  from  Poisson.  After  the  publication  (in  1825)  of  the 
fifth  volume  of  the  Mecanique  Celeste,  Laplace  became  gradually 
weaker,  and  with  it  musing  and  abstracted.  He  thought  much 
on  the  great  problems  of  existence,  and  often  muttered  to  himself 
Qii}est  ce  que  c'est  que  tout  cela !  After  many  alternations,  he 
appeared  at  last  so  permanently  prostrated  that  his  family  applied 
to  his  favorite  pupil,  M.  Poisson,  to  try  to  get  a  word  from  him. 
Poisson  paid  a  visit,  and  after  a  few  words  of  salutation,  said  '  J'ai 
une  bonne  nouvelle  a  vous  annoncer :  on  a  recu  au  Bureau  des 
Longitudes  une  lettre  d'Allemagne  annoncant  que  M.  Bessel 
a  verifie  par  1'observation  vos  decouvertes  theoriques  sur  les 
satellites  de  Jupiter.'  Laplace  opened  his  eyes  and  answered 
with  deep  gravity, '  L'homme  ne  poursuit  que  des  chimeres.'  He 
never  spoke  again.  His  death  took  place  March  5,  1827. 

The  language  used  by  the  two  great  geometers  illustrates  what 
I  have  said :  a  supreme  and  guiding  intelligence —  apart  from  a 
blind  rule  called  nature  of  things — was  an  hypothesis.  The 
absolute  denial  of  such  a  ruling  power  was  not  in  the  plan  of  the 
higher  philosophers :  it  was  left  for  the  smaller  fry.  A  round 
assertion  of  the  non-existence  of  anything  which  stands  in  the 
way  is  the  refuge  of  a  certain  class  of  minds  :  but  it  succeeds 
only  with  things  subjective  ;  the  objective  offers  resistance.  A 
philosopher  of  the  appropriative  class  tried  it  upon  the  constable 
who  appropriated  him :  I  deny  your  existence,  said  he ;  Come 
along,  all  the  same,  said  the  unpsychological  policeman. 

Euler  was  a  believer  in  Grod,  downright  and  straightforward. 
The  following  story  is  told  by  Thiebault,  in  his  Souvenirs  de 
vingt  ans  de  sejour  a  Berlin,  published  in  his  old  age,  about 
1 804.  This  volume  was  fully  received  as  trustworthy ;  and 
Marshal  Mollendorff  told  the  Due  de  Bassano  in  1 807  that  it  was 
the  most  veracious  of  books  written  by  the  most  honest  of  men. 
Thiebault  says  that  he  has  no  personal  knowledge  of  the  truth  of 
the  story,  but  that  it  was  believed  throughout  the  whole  of  the 


ROTATION   OF  THE   MOON.  251 

north  of  Europe.  Diderot  paid  a  visit  to  the  Eussian  Court  at 
the  invitation  of  the  Empress.  He  conversed  very  freely,  and 
gave  the  younger  members  of  the  Court  circle  a  good  deal  of 
lively  atheism.  The  Empress  was  much  amused,  but  some  of  her 
councillors  suggested  that  it  might  be  desirable  to  check  these 
expositions  of  doctrine.  The  Empress  did  not  like  to  put  a  direct 
muzzle  on  her  guest's  tongue,  so  the  following  plot  was  contrived. 
Diderot  was  informed  that  a  learned  mathematician  was  in  pos- 
session of  an  algebraical  demonstration  of  the  existence  cf  God, 
and  would  give  it  him  before  all  the  Court,  if  he  desired  to  hear 
it.  Diderot  gladly  consented :  though  the  name  of  the  mathe- 
matician is  not  given,  it  was  Euler.  He  advanced  towards 
Diderot,  and  said  gravely,  and  in  a  tone  of  perfect  conviction : 

ft        I       7j  ** 

Monsieur,  — — =  x,  done  Dieu  existe ;  repondez  !   Diderot, 

n 

to  whom  algebra  was  Hebrew,  was  embarrassed  and  disconcerted  5 
while  peals  of  laughter  rose  on  all  sides.  He  asked  permifesion 
to  return  to  France  at  once,  which  was  granted. 

An  examination  of  the  Astronomical  doctrine  of  the  Moon's  rota- 
tion.    By  J.  L.     Edinburgh,  1847,  8vo. 

A  systematic  attack  of  the  character  afterwards  made  with  less 
skill  and  more  notice  by  Mr.  Jellinger  Symons. 

July  1866,  J.  L.  appears  as  Mr.  James  Laurie,  with  a  new 
pamphlet  'The  Astronomical  doctrines  of  the  Moon's  rotation 
.  .  .  .'  Edinburgh.  Of  all  the  works  I  have  seen  on  the  question, 
this  is  the  most  confident,  and  the  sorest.  A  writer  on  astronomy 
said  of  Mr.  Jellinger  Symons,  '  Of  course  he  convinced  no  one  who 
knew  anything  of  the  subject.'  This  '  ungenerous  slur 'on  the 
speculator's  memory  appears  to  have  been  keenly  felt ;  but  its  truth 
is  admitted.  Those  who  knew  anything  of  the  subject  are  '  the 
so-called  men  of  science,'  whose  three  P's  were  assailed ;  prestige, 
pride,  and  prejudice :  this  the  author  tries  to  effect  for  himself 
with  three  Q's ;  quibble,  quirk,  and  quiddity.  He  explains  that 
the  Scribes  and  Pharisees  would  not  hear  Jesus,  and  that  the 
lordly  bishop  of  Eome  will  not  cast  his  tiara  and  keys  at  the  feet 
of  the  '  humble  presbyter '  who  now  plays  the  part  of  pope  in 
Scotland.  I  do  not  know  whom  he  means  :  but  perhaps  the 
friends  of  the  presbyter-pope  may  consider  this  an  ungenerous 
slur.  The  best  proof  of  the  astronomer  is  just  such  '  as  might 
have  been  expected  from  the  merest  of  blockheads ' ;  but  as  the 
giver  is  of  course  not  a  blockhead,  this  circumstance  shows  how 
deeply  blinded  by  prejudice  he  must  be. 


252  A  BUDGET  OF  PARADOXES. 

Of  course  the  paradoxers  do  not  persuade  any  persons  who  know 
their  subjects  :  and  so  these  Scribes  and  Pharisees  reject  the 
Messiah.  We  must  suppose  that  the  makers  of  this  comparison 
are  Christians  :  for  if  they  thought  the  Messiah  an  enthusiast  or 
an  impostor,  they  would  be  absurd  in  comparing  those  who  reject 
what  they  take  for  truth  with  others  who  once  rejected  what  they 
take  for  falsehood.  And  if  Christians,  they  are  both  irreverent 
and  blind  to  all  analogy.  The  Messiah,  with  His  Divine  mission 
proved  by  miracles  which  all  might  see  who  chose  to  look,  is 
degraded  into  a  prototype  of  James  Laurie,  ingeniously  astrono- 
mising  upon  ignorant  geometry  and  false  logic,  and  comparing  to 
blockheads  those  who  expose  his  nonsense.  Their  comparison  is 
as  foolish  as — supposing  them  Christians — it  is  profane  :  but,  like 
errors  in  general,  its  other  end  points  to  truth.  There  were 
Pseudochrists  and  Antichrists ;  and  a  Concordance  would  find  the 
real  forerunners  of  all  the  paradoxers.  But  they  are  not  so  clever 
as  the  old  false  prophets :  there  are  none  of  whom  we  should  be 
inclined  to  say  that,  if  it  were  possible,  they  would  deceive  the 
very  educated.  Not  an  Egyptian  among  them  all  can  make 
uproar  enough  to  collect  four  thousand  men  that  are  murderers-^- 
of  common  sense — to  lead  out  into  the  wilderness.  Nothing,  says 
the  motto  of  this  work,  is  so  difficult  to  destroy  as  the  errors  and 
false  facts  propagated  by  illustrious  men  whose  words  have 
authority.  I  deny  it  altogether.  There  are  things  much  more 
difficult  to  destroy :  it  is  much  more  difficult  to  destroy  the  truths 
and  real  facts  supported  by  such  "men.  And  again,  it  is  much 
more  difficult  to  prevent  men  of  no  authority  from  setting  up 
false  pretensions ;  and  it  is  much  more  difficult  to  destroy  asser- 
tions of  fancy  speculation.  Many  an  error  of  thought  and  learning 
has  fallen  before  a  gradual  growth  of  thoughtful  and  learned 
opposition.  But  such  things  as  the  quadrature  of  the  circle,  &c., 
are  never  put  down.  And  why  ?  Because  thought  can  influence 
thought,  but  thought  cannot  influence  self-conceit :  learning  can 
annihilate  learning  :  but  learning  cannot  annihilate  ignorance. 
A  sword  may  cut  through  an  iron  bar ;  and  the  severed  ends  will 
not  reunite :  let  it  go  through  the  air,  and  the  yielding  substance 
is  whole  again  in  a  moment. 

Miracles  versus  Nature :  being  an  application  of  certain  pro- 
positions in  the  theory  of  chances  to  the  Christian  miracles. 
By  Protimalethes.  Cambridge,  1847,  8vo. 

The  theory,  as  may  be  supposed,  is  carried  further  than  most 
students  of  the  subject  would  hold  defensible. 


THE  PLANET  NEPTUNE-STEAM  BALLOONS.  253 


An  astronomical  Lecture.  By  the  Rev.  R.  Wilson.  Greenock, 
1847,  12mo. 

Against  the  moon's  rotation  on  her  axis. 

[Handed  about  in  the  streets  in  1847 :  I  quote  the  whole  :]  Im- 
portant discovery  in  astronomy,  communicated  to  the  Astrono- 
mer Royal,  December  21st,  1846.  That  the  Sun  revolve  round 
the  Planets  in  25748|  years,  in  consequence  of  the  combined 
attraction  of  the  planets  and  their  satellites,  and  that  the  Earth 
revolve  round  the  Moon  in  18  years  and  228  days.  D.  T. 
GLAZIER  [altered  with  a  pen  into  GLAZION.]  Price  one  penny. 

1847.  In  the  United  Service  Magazine  for  September,  1847, 
Mrs.  Borron,  of  Shrewsbury,  published  some  remarks  tending  to 
impeach  the  fact  that  Neptune,  the  planet  found  by  Galle,  really 
was  the  planet  wljich  Le  Verrier  and  Adams  had  a  right  to  claim. 
This  was  followed  (September  14)  by  two  pages,  separately  circu- 
lated, of  '  Further  Observations  upon  the  Planets  Neptune  and 
Uranus,  with  a  Theory  of  Perturbations ' ;  and  (October  19, 1848) 
by  three  pages  of  'A  Keview  of  M.  Leverrier's  Exposition.' 
Several  persons,  when  the  remarkable  discovery  was  made,  con- 
tended that  the  planet  actually  discovered  was  an  intruder ;  and 
the  future  histories  of  the  discovery  must  contain  some  account  of 
this  little  after-piece.  Tim  Linkinwater's  theory  that  there  is  no 
place  like  London  for  coincidences,  would  have  been  utterly  over- 
thrown in  favour  of  what  they  used  to  call  the  celestial  spaces,  if 
there  had  been  a  planet  which  by  chance  was  put  near  the  place 
assigned  to  Neptune  at  the  time  when  the  discovery  was  made. 

Aerial  Navigation ;  containing  a  description  of  a  proposed  flying 
machine,  on  a  new  principle.  By  Daedalus  Britannicus. 
London,  1847,  8vo. 

In  1842-43  a  Mr.  Henson  had  proposed  what  he  called  an 
aeronaut  steam-engine,  and  a  Bill  was  brought  in  to  incorporate 
an  *  Aerial  Transit  Company.'  The  present  plan  is  altogether 
different,  the  moving  power  being  the  explosion  of  mixed  hydro- 
gen and  air.  Nothing  came  of  it — not  even  a  Bill.  What  the 
final  destiny  of  the  balloon  may  be  no  one  knows :  it  may  reason- 
ably be  suspected  that  difficulties  will  at  last  be  overcome. 
Darwin,  in  his  'Botanic  Garden'  (1781),  has  the  following 
prophecy : — 


254  -A  BUDGET   OF  PARADOXES. 

Soon  shall  thy  arm,  unconquered  Steam  !  afar 
Drag  the  slow  barge,  or  drive  the  rapid  car ; 
Or,  on  wide-waving  wings  expanded,  bear 
The  flying  chariot  through  the  fields  of  air. 

Darwin's  contemporaries,  no  doubt,  smiled  pity  on  the  poor  man. 
It  is  worth  note  that  the  two  true  prophecies  have  been  fulfilled 
in  a  sense  different  from  that  of  the  predictions.  Darwin  was 
thinking  of  the  suggestion  of  Jonathan  Hulls,  when  he  spoke  of 
dragging  the  slow  barge :  it  is  only  very  recently  that  the  steam- 
tug  has  been  employed  on  the  canals.  The  car  was  to  be  driven, 
not  drawn,  and  on  the  common  roads.  Perhaps,  the  flying 
chariot  will  be  something  of  a  character  which  we  cannot  imagine, 
even  with  the  two  prophecies  and  their  fulfilments  to  help  us. 

A  book  for  the  public.  New  Discovery.  The  causes  of  the 
circulation  of  the  blood  ;  and  the  true  nature  of  the  planetary 
system.  London,  1848,  8vo. 

Light  is  the  sustainer  of  motion  both  in  the  earth  and  in  the 
blood.  The  natural  standard,  the  pulse  of  a  person  in  health, 
four  beats  to  one  respiration,  gives  the  natural  second,  which  is 
the  measure  of  the  earth's  progress  in  its  daily  revolution.  The 
Greek  fable  of  the  Titans  is  an  elaborate  exposition  of  the  atomic 
theory  :  but  any  attempt  to  convince  learned  classics  would  only 
meet  their  derision ;  so  much  does  long-fostered  prejudice  stand 
in  the  way  of  truth.  The  author  complains  bitterly  that  men  of 
science  will  not  attend  to  him  and  others  like  him :  he  observes, 
that  '  in  the  time  occupied  in  declining,  a  man  of  science  might 
test  the  merits.'  This  is,  alas !  too  true ;  so  well  do  applicants 
of  this  kind  know  how  to  stick  on.  But  every  rule  has  its 
exception :  I  have  heard  of  one.  The  late  Lord  Spencer — the 
Lord  Althorp  of  the  House  of  Commons — told  me  that  a  speculator 
once  got  access  to  him  at  the  Home  Office,  and  was  proceeding  to 
unfold  his  way  of  serving  the  public.  '  I  do  not  understand  these 

things,'  said  Lord  Althorp,  '  but  I  happen  to  have (naming 

an  eminent  engineer)  upstairs ;  suppose  you  talk  to  him  on  the 
subject.'  The  discoverer  went  up,  and  in  half-an-hour  returned, 
and  said,  '  I  am  very  much  obliged  to  your  Lordship  for  intro- 
ducing me  to  Mr. ;  he  has  convinced  me  that  I  am  quite 

wrong.'  I  supposed,  when  I  heard  the  story — but  it  would  not 
have  been  seemly  to  say  it — that  Lord  A.  exhaled  candour  and 
sense,  which  infected  those  who  came  within  reach  :  he  would 
have  done  so,  if  anybody. 


THE  ANGLE  TRISECTED.  255 


A  method  to  trisect  a  series  of  angles  having  relation  to  each 
other ;  also  another  to  trisect  any  given  angle.  By  James 
Sabben.  1848  (two  quarto  pages). 

'The  consequence  of  years  of  intense  thought':  very  likely, 
and  very  sad. 

1848.  The  following  was  sent  to  me  in  manuscript.  I  give 
the  whole  of  it : — 

'  Quadrature  of  the  Circle. — A  quadrant  is  a  curvilinear  angle  tra- 
versing round  and  at  an  equal  distance  from  a  given  point,  called 
a  centre,  no  two  points  in  the  curve  being  at  the  same  angle,  but 
irreptitiously  graduating  from  90  to  60.  It  is  therefore  a  mean  angle 
of  90  and  60,  which  is  75,  because  it  is  more  than  60,  and  less  than  90, 
approximately  from  60  to  90,  and  from  90  to  60,  with  equal  generation 
in  each  irreptitious  approximation,  therefore  meeting  in  75,  and  which 
is  the  mean  angle  of  the  quadrant. 

Or,  suppose  a  line  drawn  from  a  given  point  at  90,  and  from  the 
same  point  a  line  at  60.  Let  each  of  these  lines  revolve  on  this  point 
toward  each  other  at  an  equal  ratio.  They  will  become  one  line  at  75, 
and  bisect  the  curve,  which  is  one-sixth  of  the  entire  circle.  The 
result,  taking  16  as  a  diameter,  gives  an  area  of  201  '072400,  and  a 
circumference  of  50'2681.  3  •  ] 

The  original  conception,  its  natural  harmdny,  and  the  result,  to  my 
own  mind  is  a  demonstrative  truth,  which  I  presume  it  right  to  make 
known,  though  perhaps  at  the  hazard  of  unpleasant  if  not  uncourteous 
remarks.' 

I  have  added  punctuation :  the  handwriting  and  spelling  are 
those  of  an  educated  person ;  the  word  irreptitious  is  indubitable. 
The  whole  is  a  natural  curiosity. 

The  quadrature  and  exact  area  of  the  circle  demonstrated.     By 

Wm.  Peters.     8vo.  n.  d.  (circa  1848). 

Suggestions  as  to  the  necessity  for  a  revolution  in  philosophy  ;  and 
prospectus  for  the  establishment  of  a  new  quarterly,  to  be  called 
the  Physical  Philosopher  and  Heterodox  Review.  By  Q.  E.  D. 
8vo.  1848. 

These  works  are  by  one  author,  who  also  published,  as  appears 
by  advertisement, 

'Newton  rescued  from  the  precipitancy  of  his  followers  through  a 
century  and  a  half,'  and  '  Dangers  along  a  coast  by  correcting  (as  it  is 
called)  a  ship's  reckoning  by  bearings  of  the  land  at  night  fall,  or  in 
a  fog,  nearly  out  of  print.  Subscriptions  are  requested  for  a  new 
edition.' 


256  A  BUDGET  OF  PAEADOXES. 

The  area  of  a  circle  is  made  four-fifths  of  the  circumscribed 
square :  proved  on  an  assumption  which  it  is  purposed  to  explain 
in  a  longer  essay.  The  author,  as  Q.  E.  D.,  was  in  controversy 
with  the  Athenaeum  journal,  and  criticised  a  correspondent,  D., 
who  wrote  against  a  certain  class  of  discoverers.  He  believed  the 
common  theories  of  hydrostatics  to  be  wrong,  and  one  of  his 
questions  vvas — 

'  Have  you  ever  taken  into  account  anent  gravity  and  gravitation  the 
fact  that  a  five  grain  cube  of  cork  will  of  itself  half  sink  in  the  water, 
whilst  it  will  take  20  grains  of  brass,  which  will  sink  of  itself,  to  pull 
under  the  other  half?  Fit  this  if  you  can,  friend  D.,  to  your  notions 
of  gravity  and  specific  gravity,  as  applied  to  the  construction  of  a 
universal  law  of  gravitation.' 

This  the  Athenceum  published — but  without  some  Italics,  for 
which  the  editor  was  sharply  reproved,  as  a  sufficient  specimen  of 
the  quod  erat  D.  monstrandum  :  on  which  the  author  remarks — 
4  D,— Wherefore  the  e  caret  ?  is  it  D  apostrophe  ?  D',  D'M,  D'Mo, 
D'Monstrandum ;  we  cannot  find  the  wit  of  it.'  This  I  conjecture 
to  contain  an  illusion  to  the  name  of  the  supposed  author ;  but 
whether  De  Mocritus,  De  Mosthenes,  or  De  Moivre  was  intended, 
I  am  not  willing  to  decide. 

The  Scriptural  Calendar  and  Chronological  Reformer,  for  the 
statute  year  1849.  Including  a  review  of  recent  publications 
on  the  Sabbath  question.  London,  1849,  12mo. 

This  is  the  almanac  of  a  sect  of  Christians  who  keep  the  Jewish 
Sabbath,  having  a  chapel  at  Mill  Yard,  Groodman's  Fields.  They 
wrote  controversial  works,  and  perhaps  do  so  still ;  but  I  never 
chanced  to  see  one. 

Geometry  versus  Algebra ;  or  the  trisection  of  an  angle  geometri- 
cally solved.  By  W.  Upton,  B.A.  Bath  (circa  1849).  8vo. 

The  author  published  two  tracts  under  this  title,  containing 
different  alleged  proofs:  but  neither  gives  any  notice  of  the 
change.  Both  contain  the  same  preface,  complaining  of  the 
British  Association  for  refusing  to  examine  the  production.  I 
suppose  that  the  author,  finding  his  first  proof  wrong,  invented 
the  second,  of  which  the  Association  never  had  the  offer ;  and, 
feeling  sure  that  they  would  have  equally  refused  to  examine  the 
second,  thought  it  justifiable  to  present  that  second  as  the  one 
which  they  had  refused.  Mr.  Upton  has  discovered  that  the 
common  way  of  finding  the  circumference  is  wrong,  would  set  it 


TRISECTION   OF   THE   ANGLE.  257 

right  if  he  had  leisure,  and,  in  the  mean  time,  has  solved  the 
problem  of  the  duplication  of  the  cube. 

The  trisector  of  an  angle,  if  he  demand  attention  from  any 
mathematician,  is  bound  to  produce,  from  his  construction,  an 
expression  for  the  sine  or  cosine  of  the  third  part  of  any  angle, 
in  terms  of  the  sine  or  cosine  of  the  angle  itself,  obtained  by  help 
of  no  higher  than  the  square  root.  The  mathematician  knows 
that  such  a  thing  cannot  be ;  but  the  trisector  virtually  says  it 
can  be,  and  is  bound  to  produce  it,  to  save  time.  This  is  the 
misfortune  of  most  of  the  solvers  of  the  celebrated  problems,  that 
they  have  not  knowledge  enough  to  present  those  consequences  of 
their  results  by  which  they  can  be  easily  judged.  Sometimes 
they  have  the  knowledge,  and  quibble  out  of  the  use  of  it.  In 
many  cases  a  person  makes  an  honest  beginning  and  presents  what 
he  is  sure  is  a  solution.  By  conference  with  others  he  at  last  feels 
uneasy,  fears  the  light,  and  puts  self-love  in  the  way  of  it.  Dis- 
honesty sometimes  follows.  The  speculators  are,  as  a  class,  very 
apt  to  imagine  that  the  mathematicians  are  in  fraudulent  con- 
federacy against  them :  I  ought  rather  to  say  that  each  one  of 
them  consents  to  the  mode  in  which  the  rest  are  treated,  and 
fancies  conspiracy  against  himself.  The  mania  of  conspiracy  is  a 
very  curious  subject.  I  do  not  mean  these  remarks  to  apply  to 
the  author  before  me. 

One  of  Mr.  Upton's  trisections,  if  true,  would  prove  the  truth 
of  the  following  equation  : — 

3  cos  |  =   1    +  v/  (4-sin  20) 
o 

which  is  certainly  false. 

In  1852  I  examined  a  terrific  construction,  at  the  request  of 
the  late  Dr.  "Wallich,  who  was  anxious  to  persuade  a  poor  country- 
man of  his  that  trisection  of  the  angle  was  waste  of  time.  One  of 
the  principles  was,  that  '  magnitude  and  direction  determine  each 
other.'  The  construction  was  equivalent  to  the  assertion  that, 
6  being  any  angle,  the  cosine  of  its  third  part  is 

o/j             50    ,       .      o/j      .     50 
sin  30 .  cos h  sin  id  sin  — . 

w  -i 

divided  by  the  square  root  of 

IZ.Q 
sin  230  cos  -  -  +  sin  40  +  sin  30 .  sin  59 .  sin  20 

m 

This  is  from  my  rough  notes,  and  I  believe  it  is  correct.  It 
is  so  nearly  true,  unless  the  angle  be  very  obtuse,  that  common 
drawing,  applied  to  the  construction,  will  not  detect  the  error. 


258  A  BUDGET  OF  PAKADOXES. 

There  are  many  formulae  of  this  kind  :  and  I  have  several  times 
found  a  speculator  who  has  discovered  the  corresponding  con- 
struction, has  seen  the  approximate  success  of  his  drawing — often 
as  great  as  absolute  truth  could  give  in  graphical  practice, — and 
has  then  set  about  his  demonstration,  in  which  he  always  succeeds 
to  his  own  content. 

There  is  a  trisection  of  which  I  have  lost  both  cutting  and 
reference  :  I  think  it  is  in  the  United  Service  Journal.  I  could 
not  detect  any  error  in  it,  though  certain  there  must  be  one. 
At  least  I  discovered  that  two  parts  of  the  diagram  were  incom- 
patible unless  a  certain  point  lay  in  line  with  two  others,  by 
which  the  angle  to  be  trisected — and  which  was  trisected — was 
bound  to  be  either  0°  or  180°. 

Aug.  22,  1866.  Mr.  Upton  sticks  to  his  subject.  He  has  just 
published  '  The  Uptonian  Trisection.  Eespectfully  dedicated  to 
the  schoolmasters  of  the  United  Kingdom.'  It  seems  to  be  a 
new  attempt.  He  takes  no  notice  of  the  sentence  I  have  put  in 
italics :  nor  does  he  mention  my  notice  of  him,  unless  he  mean 
to  include  me  among  those  by  whom  he  has  been  '  ridiculed  and 
sneered  at '  or  '  branded  as  a  brainless  heretic.'  I  did  neither  one 
nor  the  other :  I  thought  Mr.  Upton  a  paradoxer  to  whom  it  was 
likely  to  be  worth  while  to  propound  the  definite  assertion  now 
in  italics  ;  and  Mr.  Upton  does  not  find  it  convenient  to  take 
issue  on  the  point.  He  prefers  general  assertions  about  algebra. 
So  long  as  he  cannot  meet  algebra  on  the  above  question,  he  may 
issue  as  many  '  respectful  challenges '  to  the  mathematicians  as 
he  can  find  paper  to  write :  he  will  meet  with  no  attention. 

There  is  one  trisection  which  is  of  more  importance  than  that 
of  the  angle.  It  is  easy  to  get  half  the  paper  on  which  you 
write  for  margin ;  or  a  quarter  ;  but  very  troublesome  to  get  a 
third.  Show  us  how,  easily  and  certainly,  to  fold  the  paper  into 
three,  and  you  will  be  a  real  benefactor  to  society. 

Early  in  the  century  there  was  a  Turkish  trisector  of  the 
angle,  Hussein  Effendi,  who  published  two  methods.  He  was  the 
father  of  Ameen  Bey,  who  was  well  known  in  England  thirty 
years  ago  as  a  most  amiable  and  cultivated  gentleman  and  an 
excellent  mathematician.  He  was  then  a  student  at  Cambridge  : 

O        " 

and  he  died,  years  ago,  in  command  of  the  army  in  Syria. 
Hussein  Effendi  was  instructed  in  mathematics  by  Ingliz  Selim 
Eifendi,  who  translated  a  work  of  Bonnycastle  into  Turkish. 
This  Englishman  was  Kichard  Baily,  brother  of  Francis  Baily  the 
astronomer,  who  emigrated  to  Turkey  in  his  youth,  and  adopted 


LETTER  FROM  A  CYCLOMETER.  259 

the  manners  of  the  Turks,  but  whether  their  religion  also  I  never 
heard,  though  I  should  suppose  he  did. 

I  now  give  the  letters  from  the  agricultural  labourer  and  his 
friend,  described  in  page  9.  They  are  curiosities ;  and  the 
history  of  the  quadrature  can  never  be  well  written  without  some 
specimens  of  this  kind : — 

'  Doctor  Morgan,  Sir.     Permit  mo  to  address  you 

Brute  Creation  may  perhaps  enjoy  the  faculty  of  behold- 
ing visible  things  with  a  more  penitrating  eye  than  ourselves.  But 
Spiritual  objects  are  as  far  out  of  their  reach  as  though  they  had  no 
being 

Nearest  therefore  to  the  brute  Creation  are  those  men  who  Suppose 
themselves  to  be  so  far  governed  by  external  objects  as  to  believe 
nothing  but  what  they  See  and  feel  And  Can  accomedate  to  their 
Shallow  understanding  and  Imaginations 

My  Dear  Sir  Let  us  all  Consult  ourselves  by  the  wise  proverb.. 

I  believe  that  evry  man*  merit  &  ability  aught  to  be  appreciated 
and  valued  In  proportion  to  its  worth  &  utility 

In  whatever  State  or  Circumstances  they  may  fortunately  or  un- 
fortunately be  placed 

And  happy  it  is  for  evry  man  to  know  his  worth  and  place 

When  a  Gentleman  of  your  Standing  in  Society  Clad  with  those 
honors  Can  not  understand  or  Solve  a  problem  That  is  explicitly  ex- 
plained by  words  and  Letters  and  mathematacally  operated  by  figuers 
He  had  best  consult  the  wise  proverd 

Do  that  which  thou  Canst  understand  and  Comprehend  for  thy 
good. 

I  would  recommend  that  Such  Gentleman  Change  his  business 

And  appropriate  his  time  and  attention  to  a  Sunday  School  to 
Learn  what  he  Could  and  keep  the  Litle  Children  form  durting  their 
Close 

With  Sincere  feelings  of  Gratitude  for  your  weakness  and  Inability 
I  am 

Sir  your  Superior  in  Mathematics ' 

1849  June  th29. 

'  Dor  Morgin  Sir 

I  wrote  and  Sent  my  work  to  Professor of  State  of  • 

United  States 

I  am  now  in  the  possesion  of  the  facts  that  he  highly  approves  of 
my  work.  And  Says  he  will  Insure  me  Reward  in  the  States 

I  write  this  that  you  may  understand  that  I  have  knowledge  of  the 
unfair  way  that  I  am  treated  In  my  own  nati  County 

I  am  told  and  have  reasons  to  believe  that  it  is  the  Clergy  that  treat 
me  so  unjust. 

I  am  not  Desirious  of  heaping  Disonors  upon  my  own  nation.     But 

3  2 


260  A  BUDGET   OF  PARADOXES. 

if  I  have  to  Leave  this  kingdom  without  my  Just  dues.  The  world 
Shall  know  how  I  am  and  have  been  treated. 

I  am  Sir  Desirous  of  my 

Just  dues 

1849  July  3. 

July  7th,  1849. 

Sir,  I  have  been  given  to  understand  that  a  friend  of  mine  one  whom  I 
shall  never  be  ashamed  to  acknowledge  as  such  tho'  lowly  his  origine; 
nay  not  only  not  ashamed  but  proud  of  doing  so  for  I  am  one  of  those 
who  esteem  and  respect  a  man  according  to  his  ability  and  probity, 
deeming  with  Dr.  Watts  '  that  the  mind  is  the  standard  of  the  man,'  has 
laid  before  you  and  asked  your  opinion  of  his  extraordinary  perform- 
ance, viz.  the  quadrature  of  the  circle,  he  did  this  with  the  firmest  belief 
that  you  would  not  only  treat  the  matter  in  a  straightforward  manner 
but  with  the  conviction  that  from  your  known  or  supposed  knowledge 
of  mathematicks  would  have  given  an  upright  and  honorable  decision 
upon  the  subject ;  but  the  question  is  have  you  done  so  ?  Could  I  say 
yes  I  would  with  the  greatest  of  pleasure  and  have  congratulated  you 
upon  your  decision  whatever  it  might  have  been  but  I  am  sorry  to  say 
that  I  cannot  your  letter  is  a  paltry  evasion,  you  say  '  that  it  is  a  great 

pity  that  you  (Mr. )  should  have  attempted  this  (the  quadrature 

of  the  circle)  for  your  mathematical  knowledge  is  not  sufficient  to 
make  you  know  in  what  the  problem  consists,'  you  don't  say  in  what 
it  does  consist  according  to  your  ideas,  oh  !  no  nothing  of  the  sort,  you 
enter  into  no  disquisition  upon  the  subject  in  order  to  show  where  you 

think  Mr.  is  wrong  and  why  you  have  not  is  simply — because 

you  cannot — you  know  that  he  has  done  it  and  what  is  if  I  am  not 
wrongly  informed  you  have  been  heard  to  say  so.  He  has  done  what 
you  nor  any  other  mathematician  as  those  who  call  themselves  such 
have  done.  And  what  is  the  reason  that  you  will  not  candidly  ac- 
knowledge to  him  as  you  have  to  others  that  he  has  squared  the  circle 
shall  I  tell  you  ?  it  is  because  he  has  performed  the  feat  to  obtain  the 
glory  of  which  mathematicians  have  battled  from  time  immemorial 
that  they  might  encircle  their  brows  with  a  wreath  of  laurels  far  more 
glorious  than  ever  conqueror  won  it  is  simply  this  that  it  is  a  poor 
man  a  humble  artisan  who  has  gained  that  victory  that  you  don't  like 
to  acknowledge  it  you  don't  like  to  be  beaten  and  worse  to  acknowledge 
that  you  have  miscalculated,  you  have  in  short  too  small  a  soul  to  ac- 
knowledge that  he  is  right. 

I  was  asked  my  opinion  and  I  gave  it  unhesitatingly  in  the  affirm- 
mative  and  I  am  backed  in  my  opinion  not  only  by  Mr. a  mathe- 
matician and  watchmaker  residing  in  the  boro  of  Southwark  but  by 

no  less  an  authority  than  the  Professor  of  mathematics  of College 

United  States  Mr. and  I  presume  that  he  at  least  is 

your  equal  as  an  authority  and  Mr. says  that  the  government 

of  the  U.  S.  will  recompense  M.  D.  for  the  discovery  he  has  made  if 
so  what  a  reflection  upon  Old  england  the  boasted  land  of  freedom 


THE   MOON'S  KOTATION.  261 

the  nursery  of  the  arts  and  sciences  that  her  sons  are  obliged  to  go  to 
a  foreign  country  to  obtain  that  recompense  to  which  they  are  justly 
entitled 

In  conclusion  I  had  to  contradict  an  assertion  you  made  to  the 
effect  that  '  there  is  not  nor  ever  was  any  reward  offered  by  the 
government  of  this  country  for  the  discovery  of  the  quadrature  of  the 
circle.'  I  beg  to  inform  you  that  there  was  but  that  it  having  been 
deemed  an  impossibility  the  government  has  withdrawn  it,  I  do  this 
upon  no  less  an  authority  than  the  Marquis  of  Northampton. 

I  am,  sir,  yours ' 

Dr.  Morgan. 

Notes  on  the  Kinematic  Effects  of  Revolution  and  Rotation,  with 
reference  to  the  Motions  of  the  Moon  and  of  the  earth.  By 
Henry  Perigal,  Jun.  Esq.  London,  1846-1849,  8vo. 

On  the  misuse  of  technical  terms.  Ambiguity  of  the  terms  Rotation 
and  Revolution,  owing  to  the  double  meaning  improperly  attri- 
buted to  each  of  the  words.  (No  date  nor  place,  but  by  Mr.  Peri- 
gal,  I  have  no  doubt,  and  containing  letters  of  1849  and  1850.) 

The  moon  controversy.  Facts  v.  Definitions.  By  H.  P.,  Jun. 
London,  1856,  8vo.  (pp.  4.) 

Mr.  Henry  Perigal  helped  me  twenty  years  ago  with  the 
diagrams,  direct  from  the  lathe  to  the  wood,  for  the  article 
'  Trochoidal  Curves,'  in  the  Penny  Cyclopaedia  :  these  cuts  add 
very  greatly  to  the  value  of  the  article,  which,  indeed,  could  not 
have  been  made  intelligible  without  them.  He  has  had  many 
years'  experience,  as  an  amateur  turner,  in  combination  of  double 
and  triple  circular  motions,  and  has  published  valuable  diagrams 
in  profusion.  A  person  to  whom  the  double  circular  motion  is 
familiar  in  the  lathe  naturally  looks  upon  one  circle  moving 
upon  another  as  in  simple  motion,  if  the  second  circle  be 
fixed  to  the  revolving  radius,  so  that  one  and  the  same  point 
of  the  moving  circle  travels  upon  the  fixed  circle.  Mr.  Perigal 
commenced  his  attack  upon  the  moon  for  moving  about 
her  axis,  in  the  first  of  the  tracts  above,  ten  years  before 
Mr.  Jellinger  Symons ;  but  he  did  not  think  it  necessary  to 
make  it  a  subject  for  the  Times  newspaper.  His  familiarity 
with  combined  motions  enabled  him  to  handle  his  arguments 
much  better  than  Mr.  J.  Symons  could  do :  in  fact,  he  is  the 
clearest  assailant  of  the  lot  which  turned  out  with  Mr.  J.  Symons. 
But  he  is  as  wrong  as  the  rest.  The  assault  is  now,  I  suppose, 
abandoned,  until  it  becomes  epidemic  again.  This  it  will  do  : 
it  is  one  of  those  fallacies  which  are  very  tempting.  There  was 
a  dispute  on  the  subject  in  1748,  between  James  Ferguson 


262  A   BUDGET  OF  PAEADOXES. 

and  an  anonymous  opponent ;  and  I  think  there  have  been 
others. 

A  poet  appears  in  the  field  (July  19,  1863)  who  calls  himself 
Cyclops,  and  writes  four  octavo  pages.  He  makes  a  distinction 
between  rotation  and  revolution ;  and  his  doctrines  and  phrases 
are  so  like  those  of  Mr.  Perigal  that  he  is  a  follower  at  least. 
One  of  his  arguments  has  so  often  been  used  that  it  is  worth 
while  to  cite  it : — 

Would  Mathematical — forsooth — 
If  true,  have  failed  to  prove  its  truth  ? 
Would  not  they — if  they  could — submit 
Some  overwhelming  proofs  of  it  ? 
But  still  it  totters  proofless  !     Hence 
There's  strong  presumptive  evidence 
None  do — or  can — such  proof  propound 
Because  the  dogma  is  unsound. 
For,  were  there  means  of  doing  so, 
They  would  have  proved  it  long  ago. 

This  is  only  one  of  the  alternatives.  Proof  requires  a  person 
who  can  give  and  a  person  who  can  receive.  I  feel  inspired  to 
add  the  following  : — 

A  blind  man  said,  As  to  the  Sun, 
I'll  take  my  Bible  oath  there's  none  ; 
For  if  tbere  had  been  one  to  show 
They  would  have  shown  it  long  ago. 
How  came  he  such  a  goose  to  be  ? 
Did  he  not  know  he  couldn't  see  ? 
Not  he  ! 

The  absurdity  of  the  verses  is  in  the  argument.  The  writer 
was  not  so  ignorant  or  so  dishonest  as  to  affirm  that  nothing  had 
been  offered  by  the  other  side  as  proof ;  accordingly,  his  syllogism 
amounts  to  this  : — If  your  proposition  were  true,  you  could  have 
given  proof  satisfactory  to  me ;  but  this  you  have  not  done, 
therefore,  your  proposition  is  not  true. 

The  echoes  of  the  moon-controversy  reached  Benares  in 
1857,  in  which  year  was  there  published  a  pamphlet  'Does  the 
Moon  Eotate  ? '  in  Sanscrit  and  English.  The  arguments  are 
much  the  same  as  those  of  the  discussion  at  home. 

We  see  that  there  are  paradoxers  in  argument  as  well  as  in 
assertion  of  fact :  my  plan  does  not  bring  me  much  into  contact 
with  these  ;  but  another  instance  may  be  useful.  Sects,  whether 
religious  or  political,  give  themselves  names  which,  in  meaning, 
are  claimed  also  by  their  opponents ;  loyal,  liberal,  conservative 


3IILNER'S    'END   OF   RELIGIOUS  .CONTROVERSY.'  263 

(of  good),  &c.  have  been  severally  appropriated  by  parties.  Whig 
and  Tory  are  unobjectionable  names :  the  first — which  occurs 
in  English  ballad  as  well  as  in  Scotland — is  sour  milk ;'  the 
second  is  a  robber.  In  theology,  the  Greek  Church  is  Orthodox, 
the  Roman  is  Catholic,  the  modern  Puritan  is  Evangelical,  &c. 

The  word  Christian  (ante,  p.  147)  is  an  instance.  When  words 
begin,  they  carry  their  meanings.  The  Jews,  who  had  their 
Messiah  to  come,  and  the  followers  of  Jesus  of  Nazareth,  who 
took  Him,  for  their  Messiah,  were  both  Christians  (which  means 
Messianites) :  the  Jews  would  never  have  invented  the  term  to 
signify  Jesuans,  nor  would  the  disciples  have  invented  such  an 
ambiguous  term  for  themselves ;  had  they  done  so,  the  Jews 
would  have  disputed  it,  as  they  would  have  done  in  later  times 
if  they  had  had  fair  play.  The  Jews  of  our  day,  I  see  by  their 
newspapers,  speak  of  Jesus  Christ  as  the  Rabbi  Joshua.  But  the 
Heathens,  who  knew  little  or  nothing  about  the  Jewish  hope, 
would  naturally  apply  the  term  Christian  to  the  only  followers 
of  a  Messiah  of  whom  they  had  heard.  For  the  Jesuans  invaded 
them  in  a  missionary  way;  while  the  Jews  did  not  attempt,  at 
least  openly,  to  make  proselytes. 

All  such  words  as  Catholic,  &c.,  are  well  enough  as  mere  nomen- 
clature ;  and  the  world  falls  for  the  most  part,  into  any  names 
which  parties  choose  to  give  themselves.  Silly  people  found  in- 
ferences on  this  concession  ;  and,  as  usually  happens,  they  can 
cite  some  of  their  betters,  St.  Augustine,  a  freakish  arguer,  or, 
to  put  it  in  the  way  of  an  old  writer,  lectorem  ne  multiloquii 
tcedio  fastidiat,  Punicis  quibusdam  argutiis  recreare  solet, 
asks,  with  triumph,  to  what  chapel  a  stranger  would  be  directed, 
if  he  inquired  the  way  to  the  Catholic  assembly  ?  But  the  best 
exhibition  of  this  kind  in  our  own  century  is  that  made  by  the 
excellent  Dr.  John  Milner,  in  a  work  (first  published  in  1801  or 
1802)  which  I  suppose  still  circulates,  'The  End  of  Religious 
Controversy : '  a  startling  title  which,  so  far  as  its  truth  is 
concerned,  might  as  well  have  been  '  The  floor  of  the  bottomless 
pit.'  This  writer,  whom  every  one  of  his  readers  will  swear  to 

1  In  the  old  ballad  of  King  Alfred  and  the  Shepherd,  when  the  latter  is  tempting 
the  disguised  king  into  his  service,  he  says  : 

Of  whig  and  whey  we  have  good  store, 

And  keep  good  pease-straw  fire. 

Whig  is  then  a  preparation  of  milk.  But  another  commonly  cited  derivation  may  be 
suspected  from  the  word  whiggamor  being  used  before  whig,  as  applied  to  the  political 
party ;  whig  may  be  a  contraction.  Perhaps  both  derivations  conspired :  the  word 
whiggamor,  said  to  be  a  word  of  command  to  the  horses,  might  contract  into  whig,  and 
the  contraction  might  br  welcomed  for  its  o\vn  native  meaning. 


264  A  BUDGET   OF  PAEADOXES. 

have  been  a  worthy  soul,  though  many,  even  of  his  own  sect,  will 
not  admire  some  of  his  logic,  speaks  as  follows  : — 

'  Letter  xxv.  On  the  true  Church  being  Catholic.  In  treating 
of  this  third  mark  of  the  true  Church,  as  expressed  in  our  common 
creed,  I  feel  my  spirits  sink  within  me,  and  I  am  almost  tempted 
to  throw  away  my  pen  in  despair.  For  what  chance  is  there  of 
opening  the  eyes  of  candid  Protestants  to  the  other  marks  of  the 
Church,  if  they  are  capable  of  keeping  them  shut  to  this?  Every 
time  they  address  the  Grod  of  Truth,  either  in  solemn  worship  or 
in  private  devotion  [stretch  of  rhetoric],  they  are  forced,  each  of 
them,  to  repeat :  /  believe  in  THE  CATHOLIC  Church,  and  yet  if  I 
ask  any  of  them  the  question  :  Are  you  a  CATHOLIC  ?  he  is  sure 
to  answer  me  No,  I  am  a  PROTESTANT  !  Was  there  ever  a  more 
glaring  instance  of  inconsistency  and  self-condemnation  among 
rational  beings ! ' 

John  Milner,  honest  and  true, 

Did  what  honest  people  still  may  do, 

If  they  write  for  the  many  and  not  for  the  few, 

But  what  by  and  bye  they  must  eschew. 

He  shortened  his  clause;  and  for  a  reason.  If  he  had  used 
the  whole  epithet  which  he  knew  so  well,  any  one  might  have 
given  his  argument  a  half-turn.  Had  he  written,  as  he  ought, 
1  the  Holy  Catholic  Church '  and  then  argued  as  above,  some  sly 
Protestant  would  have  parodied  him  with  '  and  yet  if  I  ask  any 
of  them  the  question  :  Are  you  HOLY  ?  he  is  sure  to  answer  me 
No,  I  am  a  SINNER.'  To  take  the  adjective  from  the  Church,  and 
apply  it  to  the  individual  partisan,  is  recognised  slipslop,  but  not 
ground  of  argument.  If  Dr.  M.  had  asked  his  Protestant  whether 
he  belonged  to  the  Catholic  Church,  the  answer  would  have  been 
Yes,  but  not  to  the  Roman  branch.  When  he  put  his  question 
as  he  did,  he  was  rightly  answered  and  in  his  own  division.  This 
leaving  out  words  is  a  common  practice,  especially  when  the 
emitter  is  in  authority,  and  cannot  be  exposed.  A  year  or  two 
ago  a  bishop  wrote  a  snubbing  letter  to  a  poor  parson,  who  had 
complained  that  he  was  obliged,  in  burial,  to  send  the  worst  of 
sinners  to  everlasting  happiness.  The  bishop  sternly  said  '  hope  l 

1  It  will  be  said  that  when  the  final  happiness  is  spoken  of  in  '  sure  and  certain 
hope,'  it  is  the  Kesurrection,  generally  ;  but  when  afterwards  application  is  made  to 
the  individual,  simple  '  hope'  is  all  that  is  predicated  which  merely  means  '  wish  ? '  I 
know  it :  but  just  before  the  general  declaration,  it  is  declared  that  it  has  pleased  God 
of  his  great  mercy  to  take  unto  Himself,  the  soul  of  our  dear  brother :  and  between 
the  '  hopes '  hearty  thanks  are  given  that  it  has  pleased  God  to  deliver  our  dear 
Iro'.her  out  of  the  miseries  of  this  wicked  world,  with  an  additional  prayer  that  the 
number  of  the  elect  may  shortly  be  accomplished.  All  which  means,  that  our  dear 


THE  BURIAL  SERVICE.  2G5 

is  not  assurance.''  Could  the  clergyman  have  dared  to  answer,  lie 
would  have  said,  '  No,  my  Lord !  but  "  sure  and  certain  hope  "  is 
as  like  assurance  as  a  minikin  man  is  like  a  dwarf.'  Sad  to  say, 
a  theologian  must  be  illogical :  I  fell  sure  that  if  you  took  the 
clearest  headed  writer  on  logic  that  ever  lived,  and  made  a  bishop 
of  him,  he  would  be  shamed  by  his  own  books  in  a  twelvemonth. 

Milner's  sophism  is  glaring  :  but  why  should  Dr.  Milner  be 
wiser  than  St.  Augustine,  one  of  his  teachers  ?  I  am  tempted  to 
let  out  the  true  derivation  of  the  word  Catholic,  as  exclusively 
applied  to  the  Church  of  Rome.  All  can  find  it  who  have  access 
to  the  Rituale  of  Bonaventura  Piscator  (lib.  i.  c.  12,  de  nomine 
Sacrw  Ecclesice,  p.  87  of  the  Venice  folio  of  1537).  I  am  told 
that  there  is  a  Rituale  in  the  Index  Expurgatorius,  but  I  have 
not  thought  it  worth  while  to  examine  whether  this  be  the  one  : 
I  am  rather  inclined  to  think,  as  I  have  heard  elsewhere,  that  the 
book  was  held  too  dangerous  for  the  faithful  to  know  of  it,  even 
by  a  prohibition  :  it  would  not  surprise  me  at  all  if  Roman 
Christians  should  deny  its  existence.1 

It  amuses  me  to  give,  at  a  great  distance  of  time,  a  small 
Eowland  for  a  small  Oliver,  which  I  received,  de  par  VEglise,  so 
far  as  lay  in  the  Oliver-carrier  more  than  twenty  years  ago.  The 
following  contribution  of  mine  to  Notes  and  Queries  (3rd  Ser.  vi. 

brother  is  declared  to  be  taken  to  God,  to  be  in  a  place  not  so  miserable  as  this  world 
— a  description  -which  excludes  the  '  wicked  place  ' — and  to  be  of  the  elect.  Yes,  but 
it  will  be  said  again  !  do  you  not  know  that  when  this  Liturgy  was  framed,  all  who 
were  not  in  the  road  to  Heaven  were  excommunicated,  and  could  not  have  the  burial 
service  read  over  them.  Supposing  the  fact  to  have  been  true  in  old  time,  which  is  a 
very  spicy  supposition,  how  does  that  excuse  the  present  practice?  Have  you  a  right 
always  to  say  what  yon  believe  cannot  always  be  true,  because  you  think  it  was  once 
always  true?  Yes,  but,  choose  whom  you  please,  you  cannot  be  certain  He  is  not 
gone  to  Heaven.  True,  and  choose  which  Bishop  you  please,  you  cannot  be  demon- 
stratively certain,  he  is  not  a  concealed  unbeliever :  may  I  therefore  say  of  the 
whole  bench,  singulatim  et  seriatim,  that  they  are  unbelievers  ?  No  !  No  !  The  voice 
of  common  sense,  of  which  common  logic  is  a  part,  is  slowly  opening  the  eyes  of  the 
multitude  to  the  unprincipled  reasoning  of  theologians.  Remember  1819.  What 
chance  had  Parliamentary  Reform  when  the  House  of  Commons  thanked  the  Man- 
chester sabre-men  ?  If  you  dp  not  reform  your  Liturgy,  it  will  be  reformed  for  yon, 
and  sooner  than  you  think!  The  dishonest  interpretations,  by  defence  of  which  even 
the  minds  of  children  are  corrupted,  and  which  throw  their  shoots  into  literature  and 
commerce,  will  be  sent  to  the  place  whence  they  came :  and  over  the  dcor  of  the 
established  organization  for  teaching  religion  will  be  posted  the  following  notice : — 

Shift  and  Subterfuge,  Shuffle  and  Dodge, 

No  longer  here  allowed  to  lodge  ! 

All  this  ought  to  be  written  by  some  one  who  belongs  to  the  Establishment:  in  him, 
it  would  be  quite  prudent  and  proper;  in  me,  it  is  kind  and  charitable. 

1  This  derivation  lias  been  omitted  (ED.). 


266  A   BUDGET   OF  PAEADOXES. 

p.  175,  Aug.  27,  1864)  will  explain  what  I  say.  There  had  been 
a  complaint  that  a  contributor  had  used  the  term  Papist,  which 
a  very  excellent  dignitary  of  the  Papal  system  pronounced  an 
offensive  term : — 

PAPIST. 

The  term  papist  should  be  stripped  of  all  except  its  etymo- 
logical meaning,  and  applied  to  those  who  give  the  higher  and 
final  authority  to  the  declaration  ex  cathedra  of  the  Pope. 
See  Dr.  Wiseman's  article,  Catholic  Church,  in  the  Penny  Cyclo- 
paedia. 

What  is  one  to  do  about  these  names  ?  First,  it  is  clear  that 
offence  should,  when  possible,  be  avoided :  secondly,  no  one  must 
be  required  to  give  a  name  which  favours  any  assumption  made 
by  those  to  whom  it  is  given,  and  not  granted  by  those  who  give 
it.  Thus  the  subdivision  which  calls  itself  distinctively  Evan- 
gelical has  no  right  to  expect  others  to  concede  the  title.  Now 
the  word  Catholic,  of  course,  falls  under  this  rule ;  and  even 
Roman  Catholic  may  be  refused  to  those  who  would  restrict  the 
word  Catholic  to  themselves.  Roman  Christian  is  unobjec- 
tionable, since  the  Roman  Church  does  not  deny  the  name  of 
Christian  to  those  whom  she  calls  heretics.  No  one  is  bound  in 
this  matter  by  Acts  of  Parliament.  In  many  cases,  no  doubt, 
names  which  have  offensive  association  are  used  merely  by  habit, 
sometimes  by  hereditary  transmission.  Boswell  records  of 
Johnson  that  he  always  used  the  words  'dissenting  teacher,' 
refusing  minister  and  clergyman  to  all  but  the  recipients  of 
episcopal  ordination. 

This  distinctive  phrase  has  been  widely  adopted :  it  occurs 
in  the  Index  of  3rd  S.  iv.  [Notes  and  Queries'].  Here  we  find 
'Platts  (Rev.  John),  Unitarian  teacher,  412;'  the  article  indexed 
has  '  Unitarian  minister.' 

This,  of  course  is  habit :  an  intentional  refusal  of  the  word 
minister  would  never  occur  in  an  index.  I  remember  that,  when 
I  first  read  about  Sam  Johnson's  little  bit  of  exclusiveness,  I  said 
to  myself :  '  Teacher  ?  Teacher  ?  surely  I  remember  One  who  is 
often  called  teacher,  but  never  minister  or  clergyman :  have  not 
the  dissenters  got  the  best  of  it  ? 

When  I  said  that  the  Roman  Church  concedes  the  epithet 
Christians  to  Protestants,  I  did  not  mean  that  all  its  adherents 
do  the  same.  There  is,  or  was,  a  Roman  newspaper,  the  Tablet, 
which,  seven  or  eight  years  ago,  was  one  of  the  most  virulent  of 
the  party  journals.  In  it  I  read,  referring  to  some  complaint  of 


EELIGIOUS   NOMENCLATIVE.— FIDES.  267 

grievance  about  mixed  marriages,  that  if  Christians  would  marry 
Protestants  they  must  take  the  consequences.  My  memory  notes 
this  well ;  because  I  recollected,  when  T  saw  it,  that  there  was  in 
the  stable  a  horse  fit  to  run  in  the  curricle  with  this  one.  About 
seventeen  years  ago  an  Oxford  M.A.,  who  hated  mathematics  like 
a  genuine  Oxonian  of  the  last  century,  was  writing  on  education, 
and  was  compelled  to  give  some  countenance  to  the  nasty  subject. 
He  got  out  cleverly ;  for  he  gave  as  his  reason  for  the  permission, 
that  man  is  an  arithmetical,  geometrical,  and  mechanical  animal, 
as  well  as  a  rational  soul. 

The  Tablet  was  founded  by  an  old  pupil  of  mine,  Mr.  Frederic 
Lucas  ;  who  availed  himself  of  his  knowledge  of  me  to  write  some 
severe  articles — even  abusive,  I  was  told,  but  I  never  saw  them — 
against  me,  for  contributing  to  the  Dublin  Review,  and  poking 
my  heretic  nose  into  orthodox  places.  Dr.  Wiseman,  the  editor, 
came  in  for  his  share,  and  ought  to  have  got  all.  Who  ever 
blamed  the  pig  for  intruding  himself  into  the  cabin  when  the 
door  was  left  open  ?  When  Mr.  Lucas  was  my  pupil,  he  was  of 
the  Society  of  Friends — in  any  article  but  this  I  should  say 
Quaker — and  was  quiet  and  gentlemanly,  as  members  of  that 
Church — in  any  article  but  this  I  should,  from  mere  habit,  say  sect 
— usually  are.  This  is  due  to  his  memory  ;  for,  by  all  I  heard, 
when  he  changed  his  religion  he  ceased  to  be  Lucas  couchant, 
and  became  Lucas  rampant,  fanged  and  langued  gules.  (I  looked 
into  Guillim  to  see  if  my  terms  were  right :  I  could  not  find 
them ;  but  to  prove  I  have  been  there,  I  notice  that  he  calls  a 
violin  a  violent.  How  comes  the  word  to  take  this  form  ?)  I 
met  with  several  Eoman  Christians,  born  and  bred,  who  were  very 
much  annoyed  at  Mr.  Lucas  and  his  doings ;  and  said  some  severe 
things  about  new  converts  needing  kicking-straps. 

The  mention  of  Dr.  Wiseman  reminds  me  of  another  word, 
appropriated  by  Christians  to  themselves :  fides ;  the  Koman  faith 
is  fides,  and  nothing  else  ;  and  the  adherents  vtefiddtB.  Hereby 
hangs  a  retort.  When  Dr.  Wiseman  was  first  in  England,  he 
gave  a  course  of  lectures  in  defence  of  his  creed,  which  were 
thought  very  convincing  by  those  who  were  already  convinced. 
They  determined  to  give  him  a  medal,  and  there  was  a  very 
serious  discussion  about  the  legend.  Dr.  Wiseman  told  me 
himself  that  he  had  answered  to  his  subscribers  that  he  would  not 
have  the  medal  at  all  unless — (naming  some  Italian  authority, 
whom  I  forget)  approved  of  the  legend.  At  last  pro  fide  vindi- 
cata  was  chosen  :  this  may  be  read  either  in  a  Popish  or  heretical 


268  A  BUDGET  OF  PARADOXES. 

sense.  The  feminine  substantive  fides  means  confidence,  trust,  (it 
is  made  to  mean  belief},  but  fidis,  with  the  same  ablative,  fide, 
and  also  feminine,  is  a  fiddle-string.1  If  a  Latin  writer  had  had 
to  make  a  legend  signifying  '  For  the  defence  of  the  fiddle-string,' 
he  could  not  have  done  it  otherwise,  in  the  terseness  of  a  legend, 
than  by  writing  pro  fide  mndicata.  Accordingly,  when  a  Eoman 
Christian  talks  to  you  of  the  faith,  as  a  thing  which  is  his  and 
not  yours,  you  may  say  fiddle.  I  have  searched  Bonaventura 
Piscator  in  vain  for  notice  of  this  ambiguity.  But  the  Greeks 
said  fiddle ;  according  to  Suidas,  cricivSaTra-os — a  word  meaning  a 
four  stringed  instrument  played  with  a  quill — was  an  exclamation 
of  contemptuous  dissent.  How  the  wits  of  different  races  jump  I 

I  am  reminded  of  a  case  of  fides  vindicata,  which,  being  in  a 
public  letter,  responding  to  a  public  invitation,  was  not  meant  to 
be  confidential.  Some  of  the  pupils  of  University  College,  in 
which  all  subdivisions  of  religion  are  (1866;  were,  1867)  on  a 
level,  have  of  course  changed  their  views  in  after  life,  and  become 
adherents  of  various  high  churches.  On  the  occasion  of  a  dinner 
of  old  students  of  the  College,  convened  by  circular,  one  of  these 
students,  whether  then  Eoman  or  Tractarian  Christian  I  do  not 
remember,  not  content  with  simply  giving  negative  answer,  or 
none  at  all,  concocted  a  jorum  of  theological  rebuke,  and  sent  it 
to  the  Dinner  Committee.  Heyday !  said  one  of  them,  this  man 
got  out  of  bed  backwards  !  How  is  that,  said  the  rest  ?  Why,  read 
his  name  backwards,  and  you  will  see.  As  thus  read  it  was — 
No  grub  \ 

To  return  to  Notes  and  Queries.  The  substitution  in  the 
(editorial)  index  of  '  Unitarian  teacher,'  for  the  contributor's 
'  Unitarian  minister,'  struck  me  very  much.  I  have  seldom 
found  such  things  unmeaning.  But  as  the  journal  had  always 
been  free  from  editorial  sectarianisms, — and  very  apt  to  check 
the  contributor! al, — I  could  not  be  sure  in  this  case.  True  it 
was,  that  the  editor  and  publisher  had  been  changed  more  than 
a  year  before  ;  but  this  was  not  of  much  force.  Though  one 
swallow  does  not  make  a  summer,  I  have  generally  found  it 
show  that  summer  is  coming.  However,  thought  I  to  myself, 
if  this  be  Little  Shibboleth,  we  shall  have  Big  Shibboleth  by-and- 
bye.  At  last  it  came.  About  a  twelvemonth  afterwards,  (3rd  S. 
vii.  p.  36)  the  following  was  the  editorial  answer  to  the  question 

1  The  words  are  of  the  same  root,  and  hence  our  word  fiddle.  Some  suppose  this 
root  means  a  rope,  which,  as  that  to  which  you  trust,  becomes,  in  one  divergence, 
confidence  itself —just  as  rock,  and  other  words,  come  to  moan  reliance — and  .in 
another,  a  little  string. 


THE  WORD   CHURCH.  269 

when  the  establishment  was  first  called  the  '  Church  of  England 
and  Ireland  : ' — 

'  That  unmeaning  clause,  "  The  United  Church  of  England  and 
Ireland,"  which  occurs  on  the  title-page  of  The  Book  of  Common  Pratjer, 
was  first  used  at  the  commencement  of  the  present  century.  The 
authority  for  this  phrase  is  the  fifth  article  of  the  Union  of  1800  : 
"  That  the  Churches  of  England  and  Ireland  be  united  into  one 
Protestant  (!)  episcopal  Church,  to  be  called '  The  United  Church,  of 
England  and  Ireland.'  '  Of  course,  churchmen  are  not  responsible 
for  the  theology  of  Acts  of  Parliament,  especially  those  passed  during 
the  dark  ages  of  the  Georgian  era.' 

That  is  to  say,  the  journal  gives  its  adhesion  to  the  party  which 
— under  the  assumed  title  of  the  Church  of  England — claims 
for  the  endowed  corporation  for  the  support  of  religion  rights 
which  Parliament  cannot  control,  and  makes  it,  in  fact,  a  power 
above  the  State.  The  State  has  given  an  inch :  it  calls  this 
corporation  by  the  name  of  the  '  United  Church  of  England  and 
Ireland,'  as  if  neither  England  nor  Ireland  had  any  other  Church. 
The  corporation,  accordingly  aspires  to  an  ell.  But  this  the 
nation  will  only  give  with  the  aspiration  prefixed.  To  illustrate 
my  allusion  in  a  delicate  way  to  polite  ears,  I  will  relate  what 
happened  in  a  Johnian  lecture-room  at  Cambridge,  some  fifty 
years  ago,  my  informant  being  present.  A  youth  of  undue 
aspirations  was  giving  a  proposition,  and  at  last  said,  '  Let  E  F 

be  produced  to  'L  : '  Not  quite  so  far,  Mr. ,  said  the  lecturer, 

quietly,  to  the  great  amusement  of  the  class,  and  the  utter 
astonishment  of  the  aspirant,  who  knew  no  more  than  a  Tract- 
arian  the  tendency  of  his  construction. 

This  word  Church  is  made  to  have  a  very  mystical  meaning. 
The  following  dialogue  between  Ecclesiastes  and  HaBreticus, 
which  I  cannot  vouch  for,  has  often  taken  place  in  spirit,  if  not 
in  letter : — E.  The  word  Church  (sKK\t]aui)  is  never  used  in  the 
New  Testament  except  generally  or  locally  for  that  holy  and 
mystical  body  to  which  the  sacraments  and  the  ordinances  of 
Christianity  are  entrusted.  H.  Indeed !  E.  It  is  beyond  a 
doubt  (here  he  quoted  half  a  dozen  texts  in  support).  H.  Do 
you  mean  that  any  doctrine  or  ordinance  which  was  solemnly 
practised  by  the  £K<\r)(ria  is  binding  upon  you  and  me  ?  E. 
Certainly,  unless  we  would  be  cut  ofi  from  the  congregation  of 
the  faithful.  H.  Have  you  a  couple  of  hours  to  spare  ?  E. 
What  for  ?  H.  If  you  have,  I  propose  we  spend  them  in  cry- 
ing, Great  is  Diana  of  the  Ephesians !  E.  What  do  you  mean  ? 
H.  You  ought  to  know  the  solemn  service  of  the 


270  A  BUDGET   OF  PARADOXES. 

(Acts  xix.  32,  41),  at  Ephesus  ;  which  any  one  might  take  to 
be  true  Church,  by  the  more  part  not  knowing  wherefore  they 
were  come  together,  and  which  was  dismissed,  after  one  of  the 
most  sensible  sermons  ever  preached,  by  the  Eecorder.  E.  I  see 
your  meaning  :  it  is  true,  there  is  that  one  exception  !  H.  Why, 
the  Recorder's  sermon  itself  contains  another,  the  swc^os 
£KK\.r)on,a,  legislative  assembly.  E.  Ah !  the  New  Testament 
can  only  be  interpreted  by  the  Church  I  H.  I  see* !  the  Church 
interprets  itself  into  existence  out  of  the  New  Testament,  and 
then  interprets  the  New  Testament  out  of  existence  into 
itself! 

I  look  upon  all  the  Churches  as  fair  game  which  declare  of 
me  that  absque  dubio  in  wternum  peribo ;  not  for  their  presump- 
tion towards  God,  but  for  their  personal  insolence  towards  myself. 
I  find  that  their  sectaries  stare  when  I  say  this.  Why !  they  do 
not  speak  of  you  in  particular !  These  poor  reasoners  seem  to 
think  that  there  could  be  no  meaning,  as  against  me,  unless  it 
should  be  propounded  that  '  without  doubt  he  shall  perish  ever- 
lastingly, especially  A.  De  Morgan.'  But  I  hold,  with  the  school- 
men, that  '  Omuls  homo  est  animal'  in  conjunction  with  '  Sortes 
est  homo  '  amounts  to  '  Sortes  est  animal.'  But  they  do  not 
mean  it  personally  !  Every  universal  proposition  is  personal  to 
every  instance  of  the  subject.  If  this  be  not  conceded,  then  I 
retort,  in  their  own  sense  and  manner,  '  Whosoever  would  serve 
God,  before  all  things  he  must  not  pronounce  God's  decision 
upon  his  neighbour.  Which  decision,  except  everyone  leave  to 
God  himself,  without  doubt  he  is  a  bigoted  noodle.' 

The  reasoning  habit  of  the  educated  community,  in  four  cases 
out  of  five,  permits  universal  propositions  to  be  stated  at  one 
time,  and  denied,  pro  re  nata,  at  another.  '  Before  we  proceed 
to  consider  any  question  involving  physical  principles,  we  should 
set  out  with  clear  ideas  of  the  naturally  possible  and  impossible.' 
The  eminent  man  who  said  this,  when  wanting  it  for  his  views 
of  mental  education  ( ! )  never  meant  it  for  more  than  what  was 
in  hand,  never  assumed  it  in  the  researches  which  will  give  him 
to  posterity  !  I  have  heard  half-a-dozen  defences  of  his  having 
said  this,  not  one  of  which  affirmed  the  truth  of  what  was  said. 
A  worthy  clergyman  wrote  that  if  A.  B.  had  said  a  certain  thing 
the  point  in  question  would  have  been  established.  It  was  shown 
to  him  that  A.B.  had  said  it,  to  which  the  reply  was  a  refusal 
to  admit  the  point  because  A.  B.  said  it  in  a  second  pamphlet 
and  in  answer  to  objections.  And  I  might  give  fifty  such  instances 
with  very  little  search.  Always  assume  more  than  you  want ; 


PROTESTANT  AND  PAPAL  CHRISTENDOM.         271 

because  you  cannot  tell  how  much  you  may  want  :  put  what  is 
over  into  the  didn't-mean-that  basket,  or  the  extreme  case 
what-not. 

Something  near  forty  years  of  examination  of  the  theologies 
on   and  off — more    years  very   much    on    than    quite   off — have 
given  me  a  good  title — to  myself,  I  ask  no  one  else  for  leave — 
to   make   the  following  remarks  :    A    conclusion  has  premises, 
facts  or  doctrines  from  proof  or  authority,  and  mode  of  inference. 
There  may  be  invention  or  falsehood  of  premise,  with  good  logic  ; 
and  there  may  be  tenable  premise,   followed  by  bad  logic  ;  and 
there  may  be  both  .false  premise  and  bad  logic.     The  Eoman 
system  has  such  a  powerful  manufactory  of  premises,  that  bad 
logic  is  little  wanted  ;  there  is  comparatively  little  of  it.     The 
doctrine-forge  of  the  Eoman  Church  is  one  glorious  compound 
of  everything  that  could  make  Heraclitus  sob  and  Democritus 
snigger.     But  not  the  only  one.      The  Protestants,  in  tearing 
away  from  the  Church  of  Rome,  took  with  them  a  fair  quantity 
of  the  results  of  the  Roman  forge,  which   they  could   not  bring 
themselves  to  give  up.     They  had  more  in  them  of  Martin  than 
of  Jack.     But  they  would  have  no  premises,  except  from  the  New 
Testament ;  though  some  eked  out  with  a  few  general  Councils. 
The  consequence  is  that  they  have  been  obliged  to  find  such  a 
logic   as  would  bring  the  conclusions  they  require  out  of  the 
canonical  books.  And  a  queer  logic  it  is  ;  nothing  but  the  Eoman 
forge  can  be  compared  with  the  Protestant  loom.     The  picking, 
the  patching,  the  piecing,  which  goes  to  the  Protestant  termini 
ad  quem,  would  be  as  remarkable  to  the  general  eye,  as  the 
Eoman   manufacture  of  termini  a  quo,  if  it  were  not  that  the 
world  at  large  seizes  the  character  of  an  asserted  fact  better  than 
that  of  a  mode  of  inference,     A  grand  step  towards  the  deifica- 
cation  of  a  lady,  made  by  alleged   revelation   1800  years  after 
her  death,  is  of  glaring  evidence  :  two  or  three  additional  shiffle- 
shuffles  towards  defence  of  saying  the  Athanasian  curse  in  church 
and  unsaying  it  out  of  church,  are   hardly  noticed.     Swift  has 
bungled  his  satire  where  he  makes  Peter  a  party  to  finding  out 
what  he  wants,  totidem   syllabis  and  totidem  literis,  when  he 
cannot  find  it  totidem  verbis.     This  is  Protestant  method  :  the 
Eoman    plan    is   viam  faciam ;    the    Protestant    plan  is  viam 
inveniam.     The  public  at  large  begins  to  be  conversant  with  the 
ways  of  ivriggling  out,  as  shown  in  the  interpretations  of  the 
damnatory  parts  of  the  Athanasian  Creed,  the  phrases  of  the  Burial 
Service,  &c.     The  time  will  come  when  the  same    public  will 
begin  to  see  the  ways  of  ivriggling  in.  But  one  thing  at  a  time : 


272  A  BUDGET  OF  PAKADOXES. 

neither  Papal  Rome  nor  Protestant  Rome  was  built — nor  will 
be  pulled  down — in  a  day. 

The  distinction  above  drawn  between  the  two  great  antitheses 
of  Christendom  may  be  illustrated  as  follows.  Two  sets  of  little 
general  dealers  lived  opposite  to  one  another :  all  sold  milk. 
Each  vaunted  its  own  produce :  one  set  said  that  the  stuff  on  the 
other  side  the  way  was  only  chalk  and  water ;  the  other  said  that 
the  opposites  sold  all  sorts  of  filth,  of  which  calves'  brain  was  the 
least  nasty.  Now  the  fact  was  that  both  sets  sold  milk,  and  from 
the  same  dairy :  but  adulterated  with  different  sorts  of  dirty 
water :  and  both  honestly  believed  that  the  mixture  was  what 
they  were  meant  to  sell  and  ought  to  sell.  The  great  difference 
between  them,  about  which  the  apprentices  fought  each  other 
like  Trojans,  was  that  the  calves'  brain  men  poured  milk  into  the 
water,  and  the  chalk  men  poured  water  into  the  milk.  The 
Greek  and  Roman  sects  on  one  side,  the  Protestant  sects  on  the 
other,  must  all  have  churches  :  the  Greek  and  Roman  sects  pour 
the  New  Testament  into  their  churches  ;  the  Protestant  sects 
pour  their  churches  into  the  New  Testament.  The  Greek  and 
Roman  insist  upon  the  New  Testament  being  no  more  than  part 
and  parcel  of  their  churches  :  the  Protestant  insist  upon  their 
churches  being  as  much  part  and  parcel  of  the  New  Testament. 
All  dwell  vehemently  upon  the  doctrine  that  there  must  be  milk 
somewhere  ;  and  each  says — I  have  it.  The  doctrine  is  true  : 
and  can  be  verified  by  anyone  who  can  and  will  go  to  the  dairy 
for  himself.  Him  will  the  several  traders  declare  to  have  no 
milk  at  all.  They  will  bring  their  own  wares,  and  challenge  a 
trial :  they  want  nothing  but  to  name  the  judges.  To  vary  the 
metaphor,  those  who  have  looked  at  Christianity  in  open  day, 
know  that  all  who  see  it  through  painted  windows  shut  out  much 
of  the  light  of  heaven  and  colour  the  rest ;  it  matters  nothing 
that  the  stains  are  shaped  into  what  are  meant  for  saints  and 
angels. 

But  there  is  another  side  of  the  question.  To  decompose 
any  substance,  it  must  be  placed  between  the  poles  of  the  battery. 
Now  theology  is  but  one  pole  ;  philosophy  is  the  other.  No  one 
can  make  out  the  combinations  of  our  day  unless  he  read  the 
writings  both  of  the  priest  and  the  philosopher  :  and  if  any  one 
should  hold  the  first  word  offensive,  I  tell  him  that  I  mean  both 
words  to  be  significant.  In  reading  these  writings,  he  will  need 
to  bring  both  wires  together  to  find  out  what  it  is  all  about. 
Time  was  when  most  priests  were  very  explicit  about  the  fate  of 
philosophers,  and  most  philosophers  were  very  candid  about  their 


THEOLOGY  AND   PHILOSOPHY.  273 

opinion  of  priests.  But,  though  some  extremes  of  the  old  sorts 
still  remain,  there  is  now,  in  the  middle,  such  a  fusion  of  the  two 
pursuits  that  a  plain  man  is  wofully  puzzled.  The  theologian 
writes  a  philosophy  which  seems  to  tell  us  that  the  New  Testa- 
ment is  a  system  of  psychology ;  and  the  philosopher  writes  a 
Christianity  which  is  utterly  unintelligible  as  to  the  question 
whether  the  Resurrection  be  a  fact  or  a  transcendental  allegory. 
What  between  the  theologian  who  assents  to  the  Athanasian 
denunciation  in  what  seems  the  sense  of  no  denunciation,  and 
the  philosopher  who  parades  a  Christianity  which  looks  like  no 
revelation,  there  is  a  maze  which  threatens  to  have  the  only 
possible  clue  in  the  theory  that  everything  is  something  else,  and 
nothing  is  anything  at  all.  But  this  is  a  paradox  far  beyond 
my  handling  :  it  is  a  Budget  of  itself. 

Religion  and  Philosophy,  the  two  best  gifts  of  Heaven,  set  up 
in  opposition  to  each  other  at  the  revival  of  letters  ;  and  never 
did  competing  tradesmen  more  grossly  misbehave.  Bad  wishes 
and  bad  names  flew  about  like  swarms  of  wasps.  The  Athanasian 
curses  were  intended  against  philosophers ;  who,  had  they  been 
a  corporation,  with  state  powers  to  protect  them,  would  have 
formulized  a  per  contra.  But  the  tradesmen  are  beginning  to 
combine  :  they  are  civil  to  each  other ;  too  civil  by  half.  I  speak 
especially  of  Great  Britain.  Old  theology  has  run  off  to  ritualism, 
much  lamenting,  with  no  comfort  except  the  discovery  that  the 
cloak  Paul  left  at  Troas  was  a  chasuble.  Philosophy,  which 
always  had  a  little  sense  sewed  up  in  its  garments — to  pay  for  its 
funeral  ? — has  expended  a  trifle  in  accommodating  itself  to  the 
new  system.  But  the  two  are  poles  of  a  battery  ;  and  a  question 
arises. 

If  Peter  Piper  picked  a  peck  of  pepper, 

Where  is  the  peck  of  pepper  Peter  Piper  picked  ? 

If  Religion  and  Philosophy  be  the  two  poles  of  a  battery,  whose 
is  the  battery  Religion  and  Philosophy  have  been  made  the  poles 
of?  Is  the  change  in  the  relation  of  the  wires  any  presumption 
of  a  removal  of  the  managers?  We  know  pretty  well  who 
handled  the  instrument :  has  he  resigned  or  been  '  turned  out  ? 
Has  he  been  put  under  restriction  ?  A  fool  may  ask  more 
questions  than  twenty  sages  can  answer  :  but  there  is  hope  ;  for 

1  The  notion  that  the  Evil  Spirit  is  a  functionary  liable  to  be  dismissed  for  not 
attending  to  his  duty,  is,  so  far  as  my  reading  goes,  utterly  unknown  in  theology. 
My  first  wrinkle  on  the  siibject  was  the  remark  of  the  Somersetshire  farmer  upon 
Palmer  the  poisoner — '  Well !  if  the  Devil  don't  take  he,  he  didn't  ought  to  be  allowed 
to  be  devil  uo  longer.' 

T 


274  A   BUDGET   OF  PARADOXES. 

twenty  sages  cannot  ask  more  questions  than  one  reviewer  can 
answer.  I  should  like  to  see  the  opposite  sides  employed  upon 
the  question,  What  are  the  commoda,  and  what  the  pericula,  of 
the  current  approximation  of  Religion  and  Philosophy  ? 

All  this  is  very  profane  and  irreverent !  It  has  always  been  so 
held  by  those  whose  position  demands  such  holding.  To  describe 
the  Church  as  it  is  passes  for  assailing  the  Church  as  it  ought  to 
be  with  all  who  cannot  do  without  it.  In  Bedlam  a  poor  creature 
who  fancied  he  was  St.  Paul,  was  told  by  another  patient  that  he 
was  an  impostor;  the  first  maniac  lodged  a  complaint  against  the 
second  for  calling  St.  Paul  an  impostor,  which,  he  argued,  with 
much  appearance  of  sanity,  ought  not  to  be  permitted  in  a  well 
regulated  madhouse.  Nothing  could  persuade  him  that  he  had 
missed  the  question,  which  was  whether  he  was  St.  Paul.  The 
same  thing  takes  place  in  the  world  at  large.  And  especially 
must  be  noted  the  refusal  to  permit  to  the  profane  the  millionth 
part  of  the  licence  assumed  by  the  sacred.  I  give  a  sound 
churchman  the  epitaph  on  St.  John  Long  ;  the  usual  pronuncia- 
tion of  whose  name  must  be  noted — 

Behold  !  ye  quacks,  the  vengeance  strong 
On  deeds  like  yours  impinging  : 

For  here  below  lies  St.  John  Long 
Who  now  must  be  long  singeing. 

How  shameful  to  pronounce  this  of  the  poor  man  !  What,  Mr. 
Orthodox !  may  I  not  do  in  joke  to  one  pretender  what  you  do  in 
earnest — unless  you  quibble — to  all  the  millions  of  the  Ofreek 
Church,  and  a  great  many  others.  Enough  of  you  and  your 
reasoning !  Gro  and  square  the  circle  ! 

The  few  years  which  end  with  1867  have  shown,  not  merely 
the  intermediate  fusion  of  Theology  and  Philosophy  of  which  I 
have  spoken,  but  much  concentration  of  the  two  extremes,  which 
looks  like  a  gathering  of  forces  for  some  very  hard  fought 
Armageddon.  Extreme  theology  has  been  aiming  at  a  high 
Church  in  England,  which  is  to  show  a  new  front  to  all  heresy : 
and  extreme  philosophy  is  contriving  a  physical  organisation 
which  is  to  think,  and  to  show  that  mind  is  a  consequence  of 
matter,  or  thought  a  recreation  of  brain.  The  physical  speculators 
begin  with  a  possible  hypothesis,  in  which  they  aim  at  explana- 
tion :  and  so  the  bold  aspirations  of  the  author  of  the  '  Vestiges  ' 
find  standing-ground  in  the  variation  of  species  by  'natural 
selection.'  Some  relics — so  supposed — of  extremely  ancient  men 
are  brought  to  help  the  general  cause.  Only  distant  hints  are 
given  that  by  possibility  it  may  end  in  the  formation  of  all  living 


SCIENTIFIC  MATERIALISM.  275 

organisms  from  a  very  few,  if  not  from  one.  The  better  heads 
abovementioned  know  that  their  theory,  if  true,  does  not  bear 
upon  morals.  The  formation  of  solar  systems  from  a  nebular 
hypothesis,  followed  by  organisations  gradually  emerging  from 
some  curious  play  of  particles,  nay,  the  very  evolution  of  mind 
and  thought  from  such  an  apparatus,  are  all  as  consistent  with  a 
Personal  creative  power  to  whom  homage  and  obedience  are  due, 
and  who  has  declared  himself,  as  with  a  blind  Nature  of  Things. 
A  pure  materialist,  as  to  all  things  visible,  may  be  even  a  bigotted 
Christian :  this  is  not  frequent,  but  it  is  possible.  There  is  a 
proverb  which  says,  A  pig  may  fly,  but  it  isn't  a  likely  bird.  But 
when  the  psychological  speculator  comes  in,  he  often  undertakes 
to  draw  inferences  from  the  physical  conclusions,  by  joining  on 
his  tremendous  apparatus  of  a  priori  knowledge.  He  deduces 
that  he  can  do  without  a  God :  he  can  deduce  all  things  without 
any  such  necessity.  With  Occam  and  Newton  he  will  have  no 
more  causes  than  are  necessary  to  explain  phenomena  to  him : 
and  if  by  pure  head-work  combined  with  results  of  physical 
observation  he  can  construct  his  universe,  he  must  be  a  veiy 
unphilosophical  man  who  would  encumber  himself  with  a  useless 
Creator!  There  is  something  tangible  about  my  method,  says 
he ;  yours  is  vague.  He  requires  it  to  be  granted  that  his  system 
is  positive  and  that  your's  is  impositive.  So  reasoned  the  stage 
coachman  when  the  railroads  began  to  depose  him — '  If  you're 
upset  in  a  stage-coach,  why,  there  you  are !  but  if  you're  upset 
on  the  railroad,  where  are  you  ? '  The  answer  lies  in  another 
question,  Which  is  most  positive  knowledge,  (rod  deduced  from 
man  and  his  history,  or  the  postulates  of  the  few  who  think  they 
can  reason  a  priori  on  the  tacit  assumption  of  unlimited  command 
of  data  ? 

We  are  not  yet  come  to  the  existence  of  a  school  of  philoso- 
phers who  explicitly  deny  a  Creator :  but  we  are  on  the  way, 
though  common  sense  may  interpose.  There  are  always  straws 
which  show  the  direction  of  the  wind.  I  have  before  me  the 
printed  letter  of  a  medical  man — to  whose  professional  ability  I 
have  good  testimony — who  finds  the  vital  principle  in  highly 
rarefied  oxygen.  With  the  usual  logic  of  such  thinkers,  he  dis- 
misses the  '  eternal  personal  identity '  because  '  If  soul,  spirit, 
mind,  which  are  merely  modes  of  sensation,  be  the  attribute  or 
function  of  nerve-tissue,  it  cannot  possibly  have  any  existence 
apart  from  its  material  organism  ! '  How  does  he  know  this  im- 
possibility ?  If  all  the  mind  we  know  be  from  nerve-tissue,  how 
does  it  appear  that  mind  in  other  planets  may  not  be  another 

T  -2 


276  A  BUDGET  OF  PARADOXES. 

thing  ?  Nay,  when  we  '  come  to  possibilities,  does  not  his  own 
system  give  a  queer  one?  If  highly  rarefied  oxygen  be  vital 
power,  more  highly  rarefied  oxygen  may  be  more  vital  and  more 
powerful.  Where  is  this  to  stop  ?  Is  it  impossible  that  a  finite 
quantity,  rarefied  ad  infinitum,  may  be  an  Omnipotent  ?  Perhaps 
the  true  Genesis,  when  written,  will  open  with  '  In  the  beginning 
was  an  imperial  quart  of  oxygen  at  60°  of  -Fahrenheit,  and  the 
pressure  of  the  atmosphere  ;  and  this  oxygen  was  infinitely  rare- 
fied ;  and  this  oxygen  became  God.'  For  myself,  my  aspirations 
as  to  this  system  are  Manichaean.  The  quart  of  oxygen  is  the 
Ormuzd,  or  good  principle :  another  quart,  of  hydrogen,  is  the 
Ahriman,  or  evil  principle  !  My  author  says  that  his  system 
explains  Freewill  and  Immortality  so  obviously  that  it  is  difficult 
to  read  previous  speculations  with  becoming  gravity.  My  de- 
duction explains  the  conflict  of  good  and  evil  with  such  clearness 
that  no  one  can  henceforward  read  the  New  Testament  with 
becoming  reverence.  The  surgeon  whom  I  have  described  is  an 
early  bud  which  will  probably  be  nipped  by  the  frost  and  wither 
on  the  ground :  but  there  is  a  good  crop  coming.  Material 
pneuma  is  destined  to  high  functions ;  and  man  is  to  read  by 
gas-light. 

The  solar  system  truly  solved  :  demonstrating  by  the  perfect 
harmony  of  the  planets,  founded  on  the  four  universal  laws,  the 
Sun  to  be  an  electrical  space  ;  and  a  source  of  every  natural 
production  displayed  throughout  the  solar  system.  By  James 
Hopkins.  London,  1849,  8vo. 

The  author  says  : — 

'  I  am  satisfied  that  I  have  given  the  true  laws  constituting  the  Sun 
to  be  space ;  and  I  call  upon  those  disposed  to  maintain  the  contrary,  to 
give  true  laws  showing  him  to  be  a  body:  until  such  can  be  satis- 
factorily established,  I  have  an  undoubted  claim  to  the  credit  of  my 
theory, — That  the  Sun  is  an  Electric  Space,  fed  and  governed  by  the 
planets,  which  have  the  property  of  attracting  heat  from  it ;  and  the 
means  of  supplying  the  necessary  pabulum  by  their  degenerated  air 
driven  off  towards  the  central  space — the  wonderful  alembic  in  which 
it  becomes  transmuted  to  the  revivifying  necessities  of  continuous 
action ;  and  the  central  space  or  Sun  being  perfectly  electric,  has  the 
counter  property  of  repulsing  the  bodies  that  attract  it.  How  wonder- 
ful a  conception }  How  beautiful,  how  magnificent  an  arrangement  ! 

'  O  Centre  !  O  Space  !  0  Electric  Space ! ' 

1849.  Joseph  Ady  is  entitled  to  a  place  in  this  list  of  dis- 
coverers :  his  great  fault,  like  that  of  some  others,  lay  in  pushing 
his  method  too  far.  He  began  by  detecting  unclaimed  dividends. 


JOSEPH   ADY — ZADKIEL.  277 

and  disclosing  them  to  their  right  owners,  exacting  his  fee  before 
he  made  his  communication.  He  then  generalized  into  trying  to 
get  fees  from  all  of  the  name  belonging  to  a  dividend  ;  and  he 
gave  mysterious  hints  of  danger  impending.  For  instance,  he 
would  write  to  a  clergyman  that  a  legal  penalty  was  hanging 
over  him ;  and  when  the  alarmed  divine  forwarded  the  sum 
required  for  disclosure,  he  was  favoured  with  an  extract  from 
some  old  statute  or  canon,  never  repealed,  forbidding  a  clergyman 
to  be  a  member  of  a  corporation,  and  was  reminded  that  he  had 

insured  his  life  in  the Office,  which  had  a  royal  charter. 

He  was  facetious,  was  Joseph :  he  described  himself  in  his 
circulars  as  '  personally  known  to  Sir  Peter  Laurie  and  all  other 
aldermen ' ;  which  was  nearly  true,  as  he  had  been  before  most  of 
them  on  charges  of  false  pretence  ;  but  I  believe  he  was  nearly 
always  within  the  law.  Sir  James  Duke,  when  Lord  Mayor, 
having  particularly  displeased  him  by  a  decision,  his  circulars  of 
1849  contain  the  following  : — 

'  Should  you  have  cause  to  complain  of  any  party,  Sir  J.  Dake  has 
contrived  a  new  law  of  evidence,  viz.,  write  to  him,  he  will  consider 
your  letter  sufficient  proof,  and  make  the  parties  complained  of  pay 
without  judge  or  jury,  and  will  frank  you  from  every  expense.' 

I  strongly  suspect  that  Joseph  Ady  believed  in  himself. 

He  sometimes  issued  a  second  warning,  of  a  Sibylline  charac- 
ter : — 

'  Should  you  find  cause  to  complain  of  anybody,  my  voluntary 
referee,  the  Rt.  Hon.  Sir  Peter  Laurie,  Kt.,  perpetual  Deputy  Lord 
Mayer,  will  see  justice  done  you  without  any  charge  whatever :  he  and 

his  toady, .  The  accursed  of  Moses  can  hang  any  man : 

thus,  by  catching  him  alone  and  swearing  Nabotli  spake  evil  against 
God  and  the  King.  Therefore  (!)  I  admit  no  strangers  to  a  personal 
conference  without  a  prepayment  of  20s.  each.  Had  you  attended  to 
my  former  notice  you  would  have  received  twice  as  much :  neglect  this 
and  you  will  lose  all.' 

Zadkiel's  Almanac  for  1849.     Nineteenth  number. 

Raphael's  Prophetic  Almanac  for  1849.     Twenty-ninth  number. 

Reasons   for   belief  in  judicial   astrology,   and   remarks   on   the 

dangerous  character  of  popish  priestcraft.     London,  1849, 12mo. 
Astronomy  in  a  nutshell :  or  the  leading  problems  of  the   solar 

system   solved  by  simple   proportion  only,  on  the    theory  of 

magnetic  attraction.     By  Lieut.  Morrison,  R.N.    London  (s.  a.) 

12mo. 

Lieut.  Morrison  is  Zadkiel  Tao  Sze,  and  declares  himself  in 
real  earnest  an  astrologer.  There  are  a  great  many  books  on 


278  A  BUDGET   OF  PARADOXES. 

astrology,  but  I  have  not  felt  interest  enough  to  preserve  many 
of  them  which  have  come  in  my  way.  If  anything  ever  had  a 
fair  trial,  it  was  astrology.  The  idea  itself  is  natural  enough. 
A  human  being,  set  down  on  this  earth,  without  any  tradition, 
would  probably  suspect  that  the  heavenly  bodies  had  something 
to  do  with  the  guidance  of  affairs.  I  think  that  any  one  who 
tries  will  ascertain  that  the  planets  do  not  prophesy :  but  if  he 
should  find  to  the  contrary,  he  will  of  course  go  on  asking.  A 
great  many  persons  class  together  belief  in  astrology  and  belief 
in  apparitions :  the  two  things  differ  in  precisely  the  way  in 
which  a  science  of  observation  differs  from  a  science  of  experi- 
ment. Many  make  the  mistake  which  M.  le  Marquis  made  when 
he  came  too  late,  and  hoped  M.  Cassini  would  do  the  eclipse  over 
again  for  his  ladies.  The  apparition  chooses  its  own  time,  and 
comes  as  seldom  or  as  often  as  it  pleases,  be  it  departed  spirit, 
nervous  derangement,  or  imposition.  Consequently  it  can  only 
be  observed,  and  not  experimented  upon.  But  the  heavens,  if 
astrology  be  true,  are  prophesying  away  day  and  night  all  the 
year  round,  and  about  every  body.  Experiments  can  be  made, 
then,  except  only  on  rare  phenomena,  such  as  eclipses:  anybody 
may  choose  his  time  and  his  question.  This  is  the  great  differ- 
ence :  and  experiments  were  made,  century  after  century.  If 
astrology  had  been  true,  it  must  have  lasted  in  an  ever-improving 
state.  If  it  be  true,  it  is  a  truth,  and  a  useful  truth,  which  had 
experience  and  prejudice  both  in  its  favour,  and  yet  lost  ground 
as  soon  as  astronomy,  its  working  tool,  began  to  improve. 

1850.  A  letter  in  the  handwriting  of  an  educated  man,  dated 
from  a  street  in  which  it  must  be  taken  that  educated  persons 
live,  is  addressed  to  the  Secretary  of  the  Astronomical  Society 
about  a  matter  on  which  the  writer  says  '  his  professional  pursuit 
will  enable  him  to  give  a  satisfactory  reply.'  In  a  question  before 
a  court  of  law  it  is  sworn  on  one  side  that  the  moon  was  shining 
at  a  certain  hour  of  a  certain  night  on  a  certain  spot  in  London  ; 
on  the  o'her  side  it  is  affirmed  that  she  was  clouded.  The 
Secretary  is  requested  to  decide.  This  is  curious,  as  the  question 
is  not  astrological.  Persons  still  send  to  Greenwich.,  now  and 
then,  to  have  their  fortunes  told.  In  one  case,  not  very  many 
years  ago,  a  young  gentleman  begged  to  know  who  his  wife  was 
to  be,  and  what  fee  he  was  to  remit. 

Sometimes  the  astronomer  turns  conjurer  for  fun,  and  his 
prophecies  are  fulfilled.  It  is  related  of  Flamsteed  that  an  old 
woman  came  to  know  the  whereabouts  of  a  bundle  of  linen  which 


ASTROLOGY — COINCIDENCES.  279 

li;ul  strayed.     Flamsteed  drew  a  circle,  put  a  square  into  it,  and 
gravely  pointed  out  a  ditch,  near  her  cottage,  in  which  he  said  it 
would  be  found.     He  meant  to   have  ^iven  the  woman  a   little 
good  advice  when  she  came  back  :  but  she  came  back  in  great 
delight,  with  the  bundle  in  her  hand,  found  in  the  veiy  place. 
The  late  Baron   Zach   received  a  letter  from  Pons,  a  successful 
finder  of  comets,  complaining  that  for  a  certain  period  he  had 
found  no  comets,  though  he  had  searched  diligently.     Zach,  a 
man  of  much  sly  humour,  told  him  that  no  spots  had  been  seen 
on  the   sun  for   about   the    same   time — which  was   true, — and 
assured  him  that  when  the  spots  came  back,  the  comets  would 
come  with  them.     Some  time  after  he  got  a  letter  from  Pons, 
who  informed  him  with  great  satisfaction  that  he  was  quite  right, 
that  very  large  spots  had  appeared  on  the  sun,  and  that  he  had 
found  a  fine  comet  shortly  after.     I  do  not  vouch  for  the  first 
story,  but  I  have  the  second  in  Zach's  handwriting.     It  would 
mend  the  joke  exceedingly  if  some  day  a  real  relation  should  be 
established  between  comets  and  solar  spots  :  of  late  years  good 
reason  has  been  shown  for  advancing  a  connexion  between  these 
spots  and  the  earth's  magnetism.     If  the  two  things  had  been  put 
to  Zach,  he  would  probably  have  chosen  the  comets.     Here  is  a 
hint  for  a  paradox :  the  solar  spots  are  the  dead  comets,  which 
have  parted  with  their  light  and  heat  to  feed  the  sun,  as  was 
once  suggested.     I  should  not  wonder  if  I  were  too  late,  and  the 
tiling  had  been  actually  maintained.     My  list  does  not  contain 
the  twentieth  part  of  the  possible  whole. 

The  mention  of  coincidences  suggests  an  everlasting  source  of 
explanations,  applicable  to  all  that  is  extraordinary.  The  great 
paradox  of  coincidence  is  that  of  Leibnitz,  known  as  the •  pre-estab- 
lished harmony,  or  law  of  coincidences,  by  which,  separately 
and  independently,  the  body  receives  impressions,  and  the  mind 
proceeds  as  if  it  had  perceived  them  from  without.  Every  sensa- 
tion, and  the  consequent  state  of  the  soul,  are  independent  things 
01  incident  in  time  by  the  pre-established  law.  The  philosopher 
could  not  otherwise  account  far  the  connexion  of  mind  and 
matter  ;  and  he  never  goes  by  so  vulgar  a  rule  as  Wlxiferer  is,  is ; 
to  him  that  which  is  not  clear  as  to  how,  is  not  at  all.  Philoso- 
phers in  general,  who  tolerate  each  other's  theories  much  better 
than  Christians  do  each  other's  failings,  seldom  revive  Leibnitz's 
fantasy :  they  seem  to  act  upon  the  maxim  quoted  by  Father 
Eustace  from  the  Decretals,  Fadnora  osi^n<li  dam  punientur, 
jliKJttlii  diift'in  <ilf«'<in<l'i  (Ifhnif. 

The  great  ghost-paradox,  ai.d  its  tluoryof  <•<•  •••>-,  will 


280  A   BUDGET  OF  PAEADOXES. 

rise  to  the  surface  in  the  mind  of  everyone.     But  the  use  of  the 
word  coincidence  is  here  at  variance  with  its  common  meaning. 
When  A  is  constantly  happening,  and  also  B,  the   occurrence  of 
A  and  B  at  the  same  moment  is  the  mere  coincidence  which  may 
be  casualty.      But    the  case   before  us  is   that  A  is    constantly 
happening,  while  B,  when  it  does  happen,  almost  always  happens 
with  A,  and  very  rarely  without  it.     That  is  to   say,  such  is  the 
phenomenon  asserted  :  and  all  who  rationally  refer  it  to  casualty, 
affirm  that  B  is  happening  very  often  as  well  as  A,  but  that  it 
is  not  thought  worthy  of  being  recorded  except  when  A  is  simul- 
taneous.    Of  course  A  is  here  a  death,  and  B  the  spectral  appear- 
ance of  the    person  who   dies.     In    talking  of  this  subject  it  is 
necessary  to  put  out  of  the  question  all  who  play  fast  and  loose 
with  their  secret  convictions :  these  had  better  give  us  a  reason, 
when  they  feel  internal  pressure  for  explanation,  that  there  is  no 
weathercock  at  Kilve  ;  this  would  do  for  all  cases.     But  persons 
of  real  inquiry  will  see  that  first,  experience  does  not  bear  out 
the  asserted  frequency  of  the  spectre,  without  the  alleged  coinci- 
dence of  death :  and  secondly,  that  if  the  crowd  of  purely  casual 
spectres  were  so  great  that  it  is  no  wonder  that,  now  and   then 
the  person  should  have  died  at  or  near  the  moment,  we  ought  to 
expect    a  much  larger  proportion  of  cases  in  which  the  spectre 
should  come  at  the  moment  of  the  death  of  one  or  another  of  all 
the  cluster  who  are  closely  connected  with  the  original  of  the 
spectre.     But  this,  we  know,  is  almost  without  example.     It  re- 
mains   then,   for   all,  who    speculate   at   all,  to  look  upon  the 
asserted  phenomenon,  think  what  they  may  of  it,  the  thing  which 
is  to  be  explained,  as  a  connexion  in  time  of  the  death,  and  the 
simultaneous  appearance  of  the  dead.     Any  person  the  least  used 
to  the  theory  of  probabilities  will  see  that  purely  casual  coinci- 
dence, the  wrong   spectre  being  comparatively  so  rare  that  it 
may  be  said  never  to  occur,  is  not  within  the  rational  field  of 
possibility. 

The  purely  casual  coincidence,  from  which  there  is  no  escape 
except  the  actual  doctrine  of  special  providences,  carried  down  to 
a  very  low  point  of  special  intention,  requires  a  junction  of  the 
things  the  like  of  each  of  which  is  always  happening.  I  will 
give  three  instances  which  have  occurred  to  myself  within  the 
last  few  years  :  I  solemnly  vouch  for  the  literal  truth  of  every 
part  of  all  three  : 

In  August  1861,  M.  Senarmont,  of  the  French  Institute, 
wrote  to  me  to  the  effect  that  Fresnel  had  sent  to  England,  in  or 
shortly  after  1824,  a  paper  for  translation  and  insertion  in  the 


CUKIOUS   COINCIDENCES.  281 

European  Revieiv,  which  shortly  afterwards  expired.  The 
question  was  what  had  become  of  that  paper.  I  examined 
the  Eeview  at  the  Museum,  found  no  trace  of  the  paper,  and 
wrote  back  to  that  effect  at  the  Museum,  adding  that  everything 
now  depended  on  ascertaining  the  name  of  the  editor,  and  tracing 
his  papers  :  of  this  I  thought  there  was  no  chance.  I  posted  this 
letter  on  my  way  home,  at  a  Post  Office  in  the  Hampstead  Eoad 
at.  the  junction  with  Edward  Street,  on  the  opposite  side  of  which 
is  a  bookstall.  Lounging  for  a  moment  over  the  exposed  books, 
sicut  meus  est  inos,  I  saw,  within  a  few  minutes  of  the  posting 
of  the  letter,  a  little  catch-penny  book  of  anecdotes  of  Macaulay, 
which  I  bought,  and  ran  over  for  a  minute.  My  eye  was  soon 
caught  by  this  sentence  : — '  One  of  the  young  fellows  immediately 
wrote  to  the  editor  (Mr.  Walker)  of  the  European  Review.'  I 
thus  got  the  clue  by  which  I  ascertained  that  there  was  no  chance 
of  recovering  Fresnel's  paper.  Of  the  mention  of  current 
reviews,  not  one  in  a  thousand  names  the  editor. 

In  the  summer  of  1865  I  made  my  first  acquaintance  with  the 
tales  of  Nathaniel  Hawthorne,  and  the  first  I  read  was  about  the 
siege  of  Boston  in  the  War  of  Independence.  I  could  not  make 
it  out :  everybody  seemed  to  have  got  into  somebody  else's  place. 
I  was  beginning  the  second  tale,  when  a  parcel  arrived  :  it  was 
a  lot  of  old  pamphlets  and  other  rubbish,  as  he  called  it,  sent  by 
a  friend  who  had  lately  sold  his  books,  had  not  thought  it  worth 
while  to  send  these  things  for  sale,  but  thought  I  might  like  to 
look  at  them  and  possibly  keep  some.  The  first  thing  I  looked 
at  was  a  sheet  which,  being  opened,  displayed  '  A  plan  of  Boston 
and  its  environs,  shewing  the  true  situation  of  his  Majesty's 
army  and  also  that  of  the  rebels,  drawn  by  an  engineer,  at  Boston 
Oct.  1775.'  Such  detailed  plans  of  current  sieges  being  then 
uncommon,  it  is  explained  that  4  The  principal  part  of  this  plan 
was  surveyed  by  Eichard  Williams,  Lieutenant  at  Boston  ;  and 
sent  over  by  the  son  of  a  nobleman  to  his  father  in  town,  by 
whose  permission  it  wa,s  published.'  I  immediately  saw  that  my 
confusion  arose  from  my  supposing  that  the  king's  troops  were 
besieging  the  rebels,  when  it  was  just  the  other  way. 

April  1,  1853,  while  engaged  in  making  some  notes  on  a  logical 
point,  an  idea  occurred  which  was  perfectly  new  to  me,  on  the 
mode  of  conciliating  the  notions  of  omnipresence  and  indivivibi- 
lil>/  into  parts.  What  it  was  is  no  matter  here:  suffice  it  that, 
since  it  was  published  elsewhere  (in  a  paper  on  Infinity.,  Camb. 
Phil.  Trans,  vol.  xi.  p.  1)  I  have  not  had  it  produced  to  me.  I 
had  just  finished  a  paragraph  on  the  subject,  when  a  parcel  came 


282  A  BUDGET  OF  PAKADOXES. 

in  from  a  bookseller  containing  Heywood's  '  Analysis  of  Kant's 
Critick,'  1844.  On  turning  over  the  leaves  I  found  (,p.  109)  the 
identical  thought  which  up  to  this  day,  I  only  know  as  in  my 
own  paper,  or  in  Kant.  I  feel  sure  I  had  not  seen  it  before,  for 
it  is  in  Kant's  first  edition,  which  was  never  translated  to  my 
knowledge ;  and  it  does  not  appear  in  the  later  editions.  Mr. 
Hey  wood  gives  some  account  of  the  first  edition. 

In  the  broadsheet  which  gave  account  of  the  dying  scene  of 
Charles  II.,  it  is  said  that  the  Koman  Catholic  priest  was  intro- 
duced by  P.  M.  A.  C.  F.  The  chain  was  this :  the  Duchess  of 
Portsmouth  applied  to  the  Duke  of  York,  who  may  have  consulted 
his  Cordelier  confessor,  Mansuete,  about  procuring  a  priest,  and 
the  priest  was  smuggled  into  the  king's  room  by  the  Duchess  and 
Chiffinch.  Now  the  letters  "are  a  verbal  acrostic  of  Pere  Mansuete 
a  Cordelier  Friar,  and  a  syllabic  acrostic  of  PortsMouth  and 
Chif Finch.  This  is  a  singular  coincidence.  Macaulay  adopted 
the  first  interpretation,  preferring  it  to  the  second,  which  I 
brought  before  him  as  the  conjecture  of  a  near  relative  of  my 
own.  But  Mansuete  is  not  mentioned  in  his  narrative :  it  may 
well  be  doubted  whether  the  writer  of  a  broadside  for  English 
readers  would  use  Pere  instead  of  Father.  And  the  person  who 
really  '  reminded '  the  Duke  of  '  the  duty  he  owed  to  his  brother,' 
was  the  Duchess  and  not  Mansuete.  But  my  affair  is  only  with 
the  coincidence. 

But  there  are  coincidences  which  are  really  connected  without 
the  connexion  being  known  to  those  who  find  in  them  matter  of 
astonishment.  Presentiments  furnish  marked  cases:  sometimes 
there  is  no  mystery  to  those  who  have  the  clue.  In  the  Gentle- 
man's Magazine  (vol.  80,  part  2,  p.  33)  we  read,  the  subject 
being  presentiment  of  death,  as  follows  :— '  In  1778,  to  come 
nearer  the  recollection  of  survivors,  at  the  taking  of  Pondicherry, 
Captain  John  Fletcher,  Captain  De  Morgan,  and  Lieutenant 
Bosanquet,  each  distinctly  foretold  his  own  death  on  the  morning 
of  his  fate.'  I  have  no  doubt  of  all  three  ;  and  I  knew  it  of  my 
grandfather  long  before  I  read  the  above  passage.  He  saw  that 
the  battery  he  commanded  was  unduly  exposed  :  I  think  by  the 
sap  running  through  the  fort  when  produced.  He  represented 
this  to  the  engineer  officers,  and  to  the  commander-in-chief ;  the 
engineers  denied  the  truth  of  the  statement,  the  commander 
believed  them,  my  grandfather  quietly  observed  that  he  must 
make  his  will,  and  the  French  fulfilled  his  prediction.  His  will 
bore  date  the  day  of  his  deatli ;  and  I  always  thought  it  more 
remarkable  than  the  fulfilment  of  the  prophecy  that  a  soldier 


.COINCIDENCE — BETTING.  283 

should  not  consider  any  danger  short  of  one  like  the  above,  suffi- 
cient reason  to  make  his  will.  I  suppose  the  other  officers  were 
similarly  posted.  I  am  told  that  military  men  very  often  defer 
making  their  wills  until  just  before  an  action :  but  to  face  the 
ordinary  risks  intestate,  and  to  wait  until  speedy  death  must  be 
the  all  but  certain  consequence  of  a  stupid  mistake,  is  carrying 
the  principle  very  far.  In  the  matter  of  coincidences  there  are, 
as  in  other  cases,  two  wonderful  extremes  with  every  intermediate 
degree.  At  one  end  we  have  the  confident  people  who  can 
attribute  anything  to  casual  coincidence ;  who  allow  Zadok 
Imposture  and  Nathan  Coincidence  to  anoint  Solomon  Self- 
conceit  king.  At  the  other  end  we  have  those  who  see  some- 
thing very  curious  in  any  coincidence  you  please,  and  whose 
minds  yearn  for  a  deep  reason.  A  speculator  of  this  class 
happened  to  find  that  Matthew  viii.  28-33  and  Luke  viii.  26-33 
contain  the  same  account,  that  of  the  demons  entering  into  the 
swine.  Very  odd  !  chapters  tallying,  and  verses  so  nearly  :  is  the 
versification  rightly  managed  ?  Examination  is  sure  to  show 
that  there  are  monstrous  inconsistencies  in  the  mode  of  division, 
which  being  corrected,  the  verses  tally  as  well  as  the  chapters. 
And  then  how  comes  it  ?  I  cannot  go  on,  for  I  have  no  gift  at 
torturing  a  coincidence  ;  but  I  would  lay  twopence,  if  I  could 
make  a  bet — which  I  never  did  in  all  my  life — that  some  one  or 
more  of  my  readers  will  try  it.  Some  people  say  that  the  study 
of  chances  tends  to  awaken  a  spirit  of  gambling  :  I  suspect  the 
contrary.  At  any  rate,  I  myself,  the  writer  of  a  mathematical 
book  and  a  comparatively  popular  book,  have  never  laid  a  bet 
nor  played  for  a  stake,  however  small :  not  one  single  time. 

It  is  useful  to  record  such  instances  as  I  have  given,  with 
precision  and  on  the  solemn  word  of  the  recorder.  When  such  a 
story  as  that  of  Flamsteed  is  told,  a  priori  assures  us  that  it  could 
not  have  been  :  the  story  may  have  been  a  ben  trovato,  but  not 
the  bundle.  It  is  also  useful  to  establish  some  of  the  good  jokes 
which  all  take  for  inventions.  My  friend  Mr.  J.  Bellingham 
Inglis,  before  1800,  saw  the  tobacconist's  carriage  with  a  sample 
of  tobacco  in  a  shield,  and  the  motto  Quid  rides  (N  &  Q.,  3rd  S.  i. 
245).  His  father  was  able  to  tell  him  all  about  it.  The  tobac- 
conist was  Jacob  Brandon,  well  known  to  the  elder  Mr.  Inglis,  and 
the  person  who  started  the  motto,  the  instant  he  was  asked  for 
such  a  thing,  was  Harry  Calender  of  Lloyd's,  a  scholar  and  a  wit. 
My  friend  Mr.  H.  Crabb  Robinson  remembers  the  King's  Counsel 
(Samuel  Marryat)  who  took  the  motto  Causes  produce  effects^ 
when  his  success  enabled  him  to  start  a  carriage. 


284  A  BUDGET  OF  PAKADOXES, 

The  coincidences  of  errata  are  sometimes  very  remarkable  :  it 
may  be  that  the  misprint  has  a  sting.  The  death  of  Sir  W. 
Hamilton  of  Edinburgh  was  known  in  London  on  a  Thursday,  and 
the  editor  of  the  Athenceum  wrote  to  me  in  the  afternoon  for  a 
short  obituary  notice  to  appear  on  Saturday.  I  dashed  off  the 
few  lines  which  appeared  without  a  moment  to  think :  and  those 
of  my  readers  who  might  perhaps  think  me  capable  of  contriving 
errata  with  meaning  will,  I  am  sure,  allow  the  hurry,  the  occasion, 
and  my  own  peculiar  relation  to  the  departed,  as  sufficient  reasons 
for  believing  in  my  entire  innocence.  Of  course  I  could  not 
see  a  proof :  and  two  errata  occurred.  The  words  '  addition  to 
Stewart '  require  '/or  addition  to  read  edition  of.'  This  represents 
what  had  been  insisted  on  by  the  Edinburgh  publisher,  who, 
frightened  by  the  edition  of  Reid,  had  stipulated  for  a  simple 
reprint  without  notes.  Again  '  principles  of  logic  and  mathe- 
matics '  required  '/or  mathematics  read  metaphysics.'  No  four 
words  could  be  put  together  which  would  have  so  good  a  title  to 
be  Hamilton's  motto. 

April  1850,  found  in  the  letter-box,  three  loose  leaves,  well 
printed  and  over  punctuated,  being 

Chapter  VI.  Brethren,  lo  I  come,  holding  forth  the  word  of  life,  for 
so  I  am  commanded  ....  Chapter  VII.  Hear  my  prayer,  O 
generations  !  and  walk  by  the  way,  to  drink  the  waters  of  the 
river  ....  Chapter  VIII.  Hearken  o  earth,  earth,  earth,  and 
the  kings  of  the  earth,  and  their  armies  .... 

A  very  large  collection  might  be  made  of  such  apostolic 
writings.  They  go  on  well  enough  in  a  misty — meant  for  mysti- 
cal— imitation  of  St.  Paul  or  the  prophets,  until  at  last  some 
prodigious  want  of  keeping  shows  the  education  of  the  writer. 
For  example,  after  half  a  page  which  might  pass  for  Irving's 
preaching — though  a  person  to  whom  it  was  presented  as  such 
would  say  that  most  likely  the  head  and  tail  would  make  some- 
thing more  like  head  and  tail  of  it — we  are  astouaded  by  a 
declaration  from  the  Holy  Spirit,  speaking  of  himself,  that  he 
is  '  not  ashamed  of  the  Gospel  of  Christ.'  It  would  be  long  before 
we  should  find  in  educated  rhapsody — of  which  there  are  speci- 
mens enough — such  a  thing  as  a  person  of  the  Trinity  taking 
merit  for  moral  courage  enough  to  stand  where  St.  Peter  fell.  The 
following  declaration  comes  next — '  I  will  judge  between  cattle 
and  cattle,  that  use  their  tongues.' 


PERPETUAL  MOTION.  285 


The   figure   of  the  earth.     By  J.    L.    Murphy,  of  Birmingham. 
(London  and  Birmingham,  4  pages,  12mo.)  (1850  ?) 

Mr.  Murphy  invites  attention  and  objection  to  some  assertions, 
as  that  the  earth  is  prolate,  not  oblate.  '  If  the  philosopher's 
conclusion  be  right,  then  the  pole  is  the  centre  of  a  valley  (!) 
thirteen  miles  deep.'  Hence  it  would  be  very  warm.  It  is 
answer  enough  to  ask — Who  knows  that  it  is  not  ? 


A  paragraph   in   the  MS.  appears  to   have  been  inserted  in   this   place   by 
mistake     It  will  be  found  in  the  Appendix  at  the  end  of  this  volume. 


1851.  The  following  letter  was  written  by  one  of  a  class  of 
persons  whom,  after  much  experience  of  them,  I  do  not  pronounce 
insane.  But  in  this  case  the  second  sentence  gives  a  suspicion  of 
actual  delusion  of  the  senses  ;  the  third  looks  like  that  eye  for 
the  main  chance  which  passes  for  sanity  on  the  Stock  Exchange 
and  elsewhere : — 

15th  Sept.  1851. 

'  Gentlemen, — I  pray  you  take  steps  to  make  known  that  yesterday  I 
completed  my  invention  which  will  give  motion  to  every  country  on  the 
Earth; — to  move  Machinery! — the  long  sought  in  vain  'Perpetual 
Motion ' !  ! — I  was  supported  at  the  time  by  the  Queen  and  H.B.H. 
Prince  Albert.  If,  Gentlemen,  you  can  advise  me  how  to  proceed  to 
claim  the  reward,  if  any  is  offered  by  the  Government,  or  how  to  secure 
the  PATENT  for  the  machine,  or  in  any  way  assist  me  by  advice  in  this 
great  work,  I  shall  most  graciously  acknowledge  your  consideration. 

These  are  my  convictions  that  my  SEVERAL  discoveries  will  be 
realised :  and  this  great  one  can  be  at  once  acted  upon  :  although  at 
this  moment  it  only  exists  in  my  mind,  from  my  knowledge  of  certain 
fixed  principles  in  nature  : — the  Machine  I  have  not  made,  as  I  only 
completed  the  discovery  YESTERDAY,  Sunday  ! 

I  have,  &c. 
To  the  Directors  of  the 
London  University,  Gower  Street. 


286  A  BUDGET  OF  PARADOXES. 


The   Divine   Drama   of  History  and  Civilisation.     By  the  Rev. 
James  Smith,  M.A.     London,  1854,  8vo. 

I  have  several  books  on  that  great  paradox  of  our  day,  Spiri- 
tualism, but  I  shall  exclude  all  but  three.  The  bibliography  of 
this  subject  is  now  very  large.  The  question  is  one  both  of 
evidence  and  speculation  ; — Are  the  facts  true  ?  Are  they  caused 
by  spirits  ?  These  I  shall  not  enter  upon :  I  shall  merely  re- 
commend this  work  as  that  of  a  spiritualist  who  does  not  enter  on 
the  subject,  which  he  takes  for  granted,  but  applies  his  derived 
views  to  the  history  of  mankind  with  learning  and  thought.  Mr. 
Smith  was  a  man  of  a  very  peculiar  turn  of  thinking.  He  was, 
when  alive,  the  editor,  or  an  editor,  of  the  Family  Herald :  I 
say  when  alive,  to  speak  according  to  knowledge  ;  for,  if  his  own 
views  be  true,  he  may  have  a  hand  in  it  still.  The  answers  to 
correspondents,  in  his  time,  were  piquant  and  original  above  any 
I  ever  saw.  I  think  a  very  readable  book  might  be  made  out 
of  them,  resembling  '  Guesses  at  Truth  : '  the  turn  given  to  an 
inquiry  about  morals,  religion,  or  socials,  is  often  of  the  highest 
degree  of  unexpectedness  ;  the  poor  querist  would  find  himself 
right  in  a  most  unpalatable  way. 

Answers  to  correspondents,  in  newspapers,  are  very  often  the 
fag  ends  of  literature.  I  shall  never  forget  the  following.  A 
person  was  invited  to  name  a  rule  without  exception,  if  he  could : 
he  answered  '  A  man  must  be  present  when  he  is  shaved.'  A 
lady — what  right  have  ladies  to  decide  questions  about  shaving  ? 
— said  this  was  not  properly  a  rule  ;  and  the  oracle  was  consulted. 
The  editor  agreed  with  the  lady ;  he  said  that  '  a  man  must  be 
present  when  he  is  shaved '  is  not  a  rule,  but  a  fact. 

[Among  my  anonymous  communicants  is  one  who  states  that 
I  have  done  injustice  to  the  Rev.  James  Smith  in  'referring 
to  him  as  a  spiritualist,'  and  placing  his  '  Divine  Drama '  among 
paradoxes :  '  it  is  no  paradox,  nor  do  spiritualistic  views  mar  or 
weaken  the  execution  of  the  design.'  Quite  true :  for  the  design 
is  to  produce  and  enforce  '  spiritualistic  views ; '  and  leather  does 
not  mar  nor  weaken  a  shoemaker's  plan.  I  knew  Mr.  Smith 
well,  and  have  often  talked  to  him  on  the  subject :  but  more 
testimony  from  me  is  unnecessary  ;  his  book  will  speak  for  itself. 
His  peculiar  style  will  justify  a  little  more  quotation  than  is  just 
necessary  to  prove  the  point.  Looking  at  the  '  battle  of  opinion ' 
now  in  progress,  we  see  that  Mr.  Smith  was  a  prescient : — 


KEY.   JAMES   SMITH.  287 

(P.  588.)  '  From  the  general  review  of  parties  in  England, 
it  is  evident  that  no  country  in  the  world  is  better  prepared  for 
the  great  Battle  of  Opinion.  Where  else  can  the  battle  be 
fought  but  where  the  armies  are  arrayed  ?  And  here  they  all 
are,  Greek,  Eoman,  Anglican,  Scotch,  Lutheran,  Calvinist, 
Established  and  Territorial,  with  Baronial  Bishops,  and  Non- 
established  of  every  grade — churches  with  living  prophets  and 
apostles,  and  churches  with  dead  prophets  and  apostles,  and 
apostolical  churches  without  apostles,  and  philosophies  without 
either  prophets  or  apostles,  and  only  wanting  one  more,  "  the 
Christian  Church,"  like  Aaron's  rod,  to  swallow  up  and  digest 
them  all,  and  then  bud  and  flourish.  As  if  to  prepare  our  minds 
for  this  desirable  and  inevitable  consummation,  different  parties 
have  been  favoured  with  a  revival  of  that  very  spirit  of  revelation 
by  which  the  Church  itself  was  originally  founded.  There  is  a 
complete  series  of  spiritual  revelations  in  England  and  the 
United  States,  besides  mesmeric  phenomena  that  bear  a  re- 
semblance to  revelation,  and  thus  gradually  open  the  mind  of 
the  philosophical  and  infidel  classes,  as  well  as  the  professed 
believers  of  that  old  revelation  which  they  never  witnessed  in 
living  action,  to  a  better  understanding  of  that  Law  of  Nature 
(for  it  is  a  Law  of  Nature)  in  which  all  revelation  originates 
and  by  which  its  spiritual  communications  are  regulated.' 

Mr.  Smith  proceeds  to  say  that  there  are  only  thirty-five  in- 
corporated churches  -in  England,  all  formed  from  the  New  Testa- 
ment except  five,  to  each  of  which  five  he  concedes  a  revelation 
of  its  own.  The  five  are  the  Quakers,  the  Swedenborgians,  the 
Southcottians,  the  Irvingites,  and  the  Mormonites.  Of  Joanna 
Southcott  he  speaks  as  follows  : — 

(P.  592.)  '  Joanna  Southcott  is  not  very  gallantly  treated 
by  the  gentlemen  of  the  Press,  who,  we  believe,  without  knowing 
anything  about  her,  merely  pick  up  their  idea  of  her  character 
from  the  rabble.  We  once  entertained  the  same  rabble  idea  of 
her ;  but  having  read  her  works — for  we  really  have  read  them 
— we  now  regard  her  with  great  respect.  However,  there  is  a 
great  abvmdance  of  chaff  and  straw  to  her  grain ;  but  the  grain 
is  good,  and  as  we  do  not  eat  either  the  chaff  or  straw  if  we  can 
avoid  it,  nor  even  the  raw  grain,  but  thrash  it  and  winnow  it, 
and  grind  it  and  bake  it,  we  find  it,  after  undergoing  tins 
process,  not  only  very  palatable,  but  a  special  dainty  of  its  kind. 
But  the  husk  is  an  insurmountable  obstacle  to  those  learned  and 
educated  gentlemen  who  judge  of  books  entirely  by  the  style 


288  A  BUDGET   OF  PAEADOXES. 

and  the  grammar,  or  those  who  eat  grain  as  it  grows,  like  the 
cattle.  Such  men  would  reject  all  prological  revelation  ;  for 
there  never  was  and  probably  never  will  be  a  revelation  by  voice 
and  vision  communicated  in  classical  manner.  It  would  be  an 
invasion  of  the  rights  and  prerogatives  of  Humanity,  and  as 
contrary  to  the  Divine  and  the  Established  order  of  mundane 
government,  as  a  field  of  quartern  loaves  or  hot  French  rolls.' 

Mr.  Smith's  book  is  spiritualism  from  beginning  to  end ;  and 
my  anonymous  gainsayer,  honest  of  course,  is  either  ignorant  of 
the  work  he  thinks  he  has  read,  or  has  a  most  remarkable  develop- 
ment of  the  organ  of  imperception.] 

I  cut  the  following  from  a  Sunday  paper  in  1849  : — 

X.  Y. — The  Chaldeans  began  the  mathematics,  in  which  the 
Egyptians  excelled.  Then  crossing  the  sea,  by  means  of  Thales,  the 
Milesian,  they  came  into  Greece,  where  they  were  improved  very  much 
by  Pythagoras,  Anaxagoras,  and  Anopides  of  Chios.  These  were 
followed  by  Briso,  Antipho,  [two  circle- sq  ua  rer  s  ;  where  is  Euclid?] 
and  Hippocrates,  but  the  excellence  of  the  algebraic  art  was  begun  by 
Geber,  an  Arabian  astronomer,  and  was  carried  on  by  Cardanus,  Tarta- 
glia,  Clavius,  Sfcevinus,  Ghctaldus,  Herigenius,  Fran,  Van  Schooten 
[meaning  Francis  Van  Schooten],  Florida  de  Beaume,  &c. 

Bryso  was  a  mistaken  man.  Antipho  had  the  disadvantage  of 
being  in  advance  of  his  age.  He  had  the  notion  of  which  the 
modern  geometry  has  made  so  much,  that  of  a  circle  being  the 
polygon  of  an  infinitely  great  number  of  sides.  He  could  make 
no  use  of  it,  but  the  notion  itself  made  him  a  sophist  in  the 
eyes  of  Aristotle,  Eutocius,  &c.  Greber,  an  Arab  astronomer, 
and  a  reputed  conjurer  in  Europe,  seems  to  have  given  his  name 
to  unintelligible  language  in  the  word  gibberish.  At  one  time 
algebra  was  traced  to  him ;  but  very  absurdly,  though  I  have 
heard  it  suggested  that  algebra  and  gibberish  must  have  had  one 
inventor. 

Any  person  who  meddles  with  the  circle  may  find  himself  the 
crane  who  was  netted  among  the  geese  :  as  Antipho  for  one, 
and  Olivier  de  Serres  for  another.  This  last  gentleman  ascer- 
tained, by  weighing,  that  the  area  of  the  circle  is  very  nearly 
that  of  the  square  on  the  side  of  the  inscribed  equilateral 
triangle:  which  it  is,  as  near  as  3-162  ...  to  3-141.  .  .  .  He 
did  not  pretend  to  more  than  approximation  ;  but  Montucla  and 
others  misunderstood  him,  and,  still  worse,  misunderstood  their 
own  misunderstanding,  and  made  him  say  the  circle  was  exactly 


ST.   VITUS,   PATRON   OF   CYCLOMETERS.  289 

double  of  the  equilateral  triangle.  He  was  let  out  of  linibo  by 
Lacroix,  in  a  note  to  his  edition  of  Montucla's  History  of  Quad- 
rature. 

Quadratura  del  cercliio,  trisezione  dell'  angulo,  et  duplicazione  del 

cubo,    problem!    geometricamente    risolute     e   dimostrate    dal 

Beverendo    Arciprete    di    San   Vito   D.    Domenico   Anghera. 

Malta,  1854,  8vo. 
Equazioni  geometriche,  estratte  dalla  lettera  del  Rev.  Arciprete  .  . 

al  Professore  Pullicino   sulla  quadratura  del  cerchio.     Milan, 

1855  or  1856,  8vo. 
H  Mediterraneo  gazetta  di  Malta,  26  Decembre  1855,  No.  909 : 

also  911,  912,  913,  914,  936,  939. 
The  Malta  Times,  Tuesday,  9th  June  1857. 
Misura  esatta  del  cerchio,  dal  Rev.    D.  Anghera.     Malta,  1857, 

12mo. 
Quadrature  of  the  circle  ...  by  the  Rev.  D.  Anghera,  Archpriest 

of  St.  Vito.     Malta,  1858,  12mo. 

I  have  looked  for  St.  Vitus  in  catalogues  of  saints,  but  never 
found  his  legend,  though  he  figures  as  a  day-mark  in  the  oldest 
almanacs.  He  must  be  properly  accredited,  since  he  has  an  arch- 
priest.  And  I  pronounce  and  ordain,  by  right  accruing  from  the 
trouble  I  have  taken  in  this  subject,  that  he,  St.  Vitus,  who  leads 
his  votaries  a  never-ending  and  unmeaning  dance,  shall  henceforth 
be  held  and  taken  to  be  the  patron  saint  of  the  circle-squarer. 
His  day  is  the  15th  of  June,  which  is  also  that  of  St.  Modestus, 
with  whom  the  said  circle-squarer  often  has  nothing  to  do.  And  . 
he  must  not  put  himself  under  the  first  saint  with  a  slanten- 
dicular  reference  to  the  other,  as  is  much  to  be  feared  was  done 
by  the  Cardinal  who  came  to  govern  England  with  a  title  con- 
taining St.  Pudentiana,  who  shares  a  day  with  St.  Dunatan. 
The  Archpriest  of  St.  Vitus  will  have  it  that  the  square  inscribed 
in  a  semicircle  is  half  of  the  semicircle,  or  the  circumference 
3£  diameters.  He  is  active  and  able,  with  nothing  wrong  about 
him  except  his  paradoxes.  In  the  second  tract  named  he  has 
given  the  testimonials  of  crowned  heads  and  ministers,  &c.  as 
follows.  Louis-Napoleon  gives  thanks.  The  minister  at  Turin 
refers  it  to  the  Academy  of  Sciences,  and  hopes  so  much  labour 
will  be  judged  degna  di  preglo.  The  Vice-Chancellor  of  Oxford 
— a  blunt  Englishman — begs  to  say  that  the  University  has  never 
proposed  the  problem,  as  some  affirm.  The  Prince  Regent  of 
Baden  has  received  the  work  with  lively  interest.  The  Academy 
of  Vienna  is  not  in  a  position  to  enter  into  the  question.  The 

U 


290  A  BUDGET   OF  PARADOXES. 

Academy  of  Turin  offers  the  most  distinct  thanks.  The  Academy 
della  Crusca  attends  only  to  literature,  but  gives  thanks.  The 
Queen  of  Spain  has  received  the  work  with  the  highest  apprecia- 
tion. The  University  of  Salamanca  gives  infinite  thanks,  and 
feels  true  satisfaction  in  having  the  book.  Lord  Palmerston 
gives  thanks,  by  the  hand  of  '  William  San.'  The  Viceroy  of 
Egypt,  not  being  yet  up  in  Italian,  will  spend  his  first  moments 
of  leisure  in  studying  the  book,  when  it  shall  have  been  trans- 
lated into  French :  in  the  mean  time  he  congratulates  the  author 
upon  his  victory  over  a  problem  so  long  held  insoluble.  All  this 
is  seriously  published  as  a  rate  in  aid  of  demonstration.  If  these 
royal  compliments  cannot  make  the  circumference  of  a  circle 
about  2  per  cent,  larger  than  geometry  will  have  it — which  is 
all  that  is  wanted — no  wonder  that  thrones  are  shaky. 

I  am  informed  that  the  legend  of  St.  Vitus  is  given  by 
Eibadeneira  in  his  lives  of  the  Saints,  and  that  Baronius,  in  his 
Martyrologium  Romanum,  refers  to  several  authors  who  have 
written  concerning  him.  There  is  an  account  in  Mrs.  Jameson's 
'History  of  Sacred  and  Legendary  Art'  (ed.  of  1863,  p.  544). 
But  it  seems  that  St.  Vitus  is  the  patron  saint  of  all  dances ;  so 
that  I  was  not  so  far  wrong  in  making  him  the  protector  of  the 
cyclometers.  Why  he  is  represented  with  a  cock  is  a  disputed 
point,  which  is  now  made  clear :  next  after  gallus  gallinaceus 
himself,  there  is  no  crower  like  the  circle-squarer. 

The  following  is  an  extract  from  the  English  Cyclopaedia, 
Art.  TABLES  : — 

'  1853.  William  Shanks,  "  Contributions  to  Mathematics,  com- 
prising chiefly  the  Rectification  of  the  Circle  to  607  Places  of  Tables," 
London,  1853.  (QUADRATURE  OF  THE  CIRCLE.)  Here  is  a  table, 
because  it  tabulates  the  results  of  the  subordinate  steps  of  this 
enormous  calculation  as  far  as  527  decimals :  the  remainder  being 
added  as  results  only  during  the  printing.  For  instance,  one  step  is  the 
calculation  of  the  reciprocal  of  601. 5601  ;  and  the  result  is  given.  The 
number  of  pages  required  to  describe  these  results  is  87.  Mr.  Shanks 
has  also  thrown  off,  as  chips  or  splinters,  the  values  of  the  base  of 
Napier's  logarithms,  and  of  its  logarithms  of  2,  3,  5,  10,  to  137  deci- 
mals ;  and  the  value  of  the  modulus  '4342.  ...  to  136  decimals;  with 
the  13th,  25th,  37tli  ...  up  to  the  721st  powers  of  2.  These  tremen 
dous  stretches  of  calculation — at  least  we  so  call  them  in  our  day — are 
useful  in  several  respects  ;  they  prove  more  than  the  capacity  of  this 
or  that  computer  for  labour  and  accuracy  ;  they  show  that  there  is  in 
the  community  an  increase  of  skill  and  courage.  We  say  in  the 
community  :  we  fully  believe  that  the  unequalled  turnip  which  every 
now  and  then  appears  in  the  newspapers  is  a  sufficient  presumption 


MR,  SHANKS'   QUADRATURE.  291 

that  the  average  turnip  is  growing  bigger,  and  the  whole  crop  heavier. 
All  who  know  the  history  of  the  quadrature  are  aware  that  the  several 
increases  of  numbers  of  decimals  to  which  IT  has  been  carried  have 
been  indications  of  a  general  increase  in  the  power  to  calculate,  and  in 
courage  to  face  the  labour.  Here  is  a  comparison  of  two  different 
times.  In  the  day  of  Cocker,  the  pupil  was  directed  to  perform  a, 
common  subtraction  with  a  voice-accompaniment  of  this  kind :  "  7  from 

4  I  cannot,  but  add  10,  7  from  14  remains  7,  set  down  7  and  carry  1 ; 
8  and  1  which  I  carry  is  9,  9  from  2  I  cannot,  &c."      We  have  before 
us   the   announcement   of  the  following   table,  undated,    as   open   to 
inspection  at  the  Crystal  Palace,  Sydenham,  in  two  diagrams  of  7  ft. 
2  in.  by  6  ft.  6  in. : — "  The  figure  9  involved  into  the  912th  power,  and 
antecedent  powers  or  involutions,  containing  upwards  of  73,000  fignres. 
Also,  the  proofs  of  the  above,  containing  upwards  of  146,000  figures. 
By  Samuel  Fancourt,  of  Mincing  Lane,  London,  and  completed  by  him. 
in  the  year  1837,  at  the  age  of  sixteen.     N.B.  The  whole  operation 
performed  by  simple  arithmetic."      The  young  operator  calculated  by 
successive  squaring  the  2nd,  4th,  8th,  &c.,  powers  up  to  the  512th,  with 
proof  by  division.      But  511  multiplications  .by  9,  in  the  short  (or 
10-1)    way,  would  have  been  much  easier.     The  2nd,  32nd,  64th, 
128th,  256th,  and  512th  powers  are  given  at  the  back  of  the  announce- 
ment.    The  powers  of  2  have  been  calculated  for  many  purposes.      In 
vol.  ii.  of  his  "  Magia  Universalis  Nature  et  Artis,"  Herbipoli,  1658, 
4to.,  the  Jesuit   Gaspar  Schott  having  discovered,  on  some  grounds  of 
theological  magic,  that  the  degrees  of  grace  of  the  Virgin  Mary  were 
in  number  the  256th   power  of  2,  calculated  that  number.     Whether 
or   no  his    number    correctly  represented  the    result    he  announced, 
he    certainly   calculated   it  rightly,  as    we  find  by  comparison    with 
Mr.  Shanks.' 

There  is  a  point  about  Mr.  Shanks'  608  figures  of  the  value 
of  TT  which  attracts  attention,  perhaps  without  deserving  it.  It 
might  be  expected  that,  in  so  many  figures,  the  nine  digits  and 
the  cipher  would  occur  each  about  the  same  number  of  times ; 
that  iSj  each  about  61  times.  But  the  fact  stands  thus  :  3  occurs 
68  times ;  9  and  2  occur  67  times  each  ;  4  occurs  64  times ;  1 
and  6  occur  62  times  each;  0  occurs  60  times;  8  occurs  58  times; 

5  occurs  56  times  ;  and  7  occurs  only  44  times.     Now,  if  all  the 
digits  were  equally  likely,  and  608  drawings  were  made,  it  is  45 
to    1  against  the  number  of  sevens  being  as  distant  from  the 
probable  average  (say  61)  as  44  on  one  side  or  78  on  the  other. 
There  must  be  some  reason  why  the  number  7  is  thus  deprived  of 
its  fair  share  in  the  structure.     Here  is  a  field  of  speculation  in 
which  two  branches  of  inquirers  might  unite.     There  is  but  one 
number  which  is  treated  with  an  unfairness  which  is  incredible 
as  an  accident  :  and  that  number  is  the  mystic  number  seven  1 


292  A   BUDGET   OF  PARADOXES. 

If  the  cyclometers  and  the  apocalyptics  would  lay  their  heads 
together  until  they  come  to  a  unanimous  verdict  on  this  pheno- 
menon, and  would  publish  nothing  until  they  are  of  one  mind, 
they  would  earn  the  gratitude  of  their  race. — I  was  wrong  :  it  is 
the  Pyramid-speculator  who  should  have  been  appealed  to.  A 
correspondent  of  my  friend  Prof.  Piazzi  Smyth  notices  that  3  is 
the  number  of  most  frequency,  and  that  3^-  is  the  nearest  approxi- 
mation to  it  in  simple  digits.  Prof.  Smyth  himself,  whose  word 
on  Egypt  is  paradox  of  a  very  high  order,  backed  by  a  great 
quantity  of  useful  labour,  the  results  of  which  will  be  made 
available  by  those  who  do  not  receive  the  paradoxes,  is  inclined 
to  see  confirmation  for  some  of  his  theory  in  these  phenomena. 

These  parad&xes  of  calculation  sometimes  appear  as  illustrations 
of  the  value  of  a  new  method.  In  1863,  Mr.  G.  Suffield,  M.A. 
and  Mr.  J.  E.  Lunn,  M.A.,  of  Clare  College  and  of  St.  John's 
College,  Cambridge,  published  the  whole  quotient  of  10000  .  .  . 
divided  by  7699,  throughout  the  whole  of  one  of  the  recurring 
periods,  having  7698  digits.  This  was  done  in  illustration  of 
Mr.  Suffield's  method  of  Synthetic  division. 

Another  instance  of  computation  carried  paradoxical  length,  in 
order  to  illustrate  a  method,  is  the  solution  of  a?3  — 2#  =  5,  the 
example  given  of  Newton's  method,  on  which  all  improvements 
have  been  tested.  In  1831,  Fourier's  posthumous  work  on  equa- 
tions showed  33  figures  of  solution,  got  with  enormous  labour. 
Thinking  this  a  good  opportunity  to  illustrate  the  superiority  of 
the  method  of  W.  Gr.  Homer,  not  then  known  in  France,  and 
not  much  known  in  England,  I  proposed  to  one  of  my  classes,  in 
1841,  to  beat  Fourier  on  this  point,  as  a  Christmas  exercise.  I 
received  several  answers,  agreeing  with  each  other,  to  50  places 
of  decimals.  In  1848,  I  repeated  the  proposal,  requesting  that 
50  places  might  be  exceeded :  I  obtained  answers  of  75,  65,  63, 
58,  57,  and  52  places.  But  one  answer,  by  Mr.  W.  Harris  John- 
ston, of  Dundalk,  and  of  the  Excise  Office,  went  to  101  decimal 
places.  To  test  the  accuracy  of  this,  I  requested  Mr.  Johnston  to 
undertake  another  equation,  connected  with  the  former  one  in  a 
way  which  I  did  not  explain.  His  solution  verified  the  former 
one,  but  he  was  unable  to  see  the  connexion,  even  when  his 
result  was  obtained.  My  reader  may  be  as  much  at  a  loss  :  the 
two  solutions  are — 

2-0945514815423265  .  .  . 

9-0544851845767340  .  .  . 

The  results  are  published  in  the  Mathematician,  vol.  iii.  p.  290. 


HORNER'S  METHOD-COMETS.  293 

In  1851,  another  pupil  of  mine,  Mr.  J.  Power  Hicks,  carried  the 
result  to  152  decimal  places,  without  knowing  what  Mr.  Johnston 
had  done.  The  result  is  in  the  English  Cyclopcedia,  article 
INVOLUTION  AND  EVOLUTION. 

I  remark  that  when  I  write  the  initial  of  a  Christian  name,  the 
most  usual  name  of  that  initial  is  understood.  I  never  saw  the 
name  of  W.  Gr.  Horner  written  at  length,  until  I  applied  to  a 
relative  of  his,  who  told  me  that  he  was,  as  I  supposed,  Wm. 
George,  but  that  he  was  named  after  a  relative  of  that  surname. 

The  square  root  of  2,  to  110  decimal  places,  was  given  me  in 
1852  by  my  pupil,  Mr.  William  Henry  Colvill,  now  (1867)  Civil 
Surgeon  at  Baghdad.  It  was 

1-4142135623730950488016887242096980785696 
7187537694807317667973799073247846210703 
885038753432  764157273501384623 

Mr.  James  Steel  of  Birkenhead  verified  thia  by  actual  multipli- 
cation, and  produced 

2  _  2580413 

1011? 
as  the  square. 

Calcolo  decidozzinale  del  Barone  Silvio  Ferrari.    Turin,  1854,  4to. 

This  is  a  serious  proposal  to  alter  our  numeral  system  and  to 
count  by  twelves.  Thus  10  would  be  twelve,  11  thirteen,  &c., 
two  new  symbols  being  invented  for  ten  and  eleven.  The  names 
of  numbers  must  of  course  be  changed.  There  are  persons  who 
think  such  changes  practicable.  I  thought  this  proposal  absurd 
when  I  first  saw  it,  and  I  think  so  still :  but  the  one  I  shall 
presently  describe  beats  it  so  completely  in  that  point,  that  I 
have  not  a  smile  left  for  this  one. 


The    successful  and  thei'efore  probably  true    theory  of   Comets. 
London,  1854.     (4  pp.  duodecimo.) 

The  author  is  the  late  Mr.  Peter  Legh,  of  Norbury  Booths 
Hall,  Knutsford,  who  published  for  eight  or  ten  years  the  Ombro- 
logical  Almanac,  a  work  of  asserted  discovery  in  meteorology. 
The  theory  of  comets  is  that  the  joint  attraction  of  the  new 
moon  and  several  planets  in  the  direction  of  the  sun,  draws  off 
the  gases  from  the  earth,  and  forms  these  cometic  meteors.  But 
how  these  meteors  come  to  describe  orbits  round  the  sun,  and  to 


204  A  BUDGET   OF  PARADOXES. 

become  capable   of  having   their   returns   predicted,   is  not  ex- 
plained. 

The  Mormon,  New  York,  Saturday,  Oct.  27,  1855. 

A  newspaper  headed  by  a  grand  picture  of  starred  and  striped 
banners,  beehive,  and  eagle  surmounting  it.  A  scroll  on  each 
side :  on  the  left,  '  Mormon  creed.  Mind  your  own  business. 
Brigham  Young ; '  on  the  right,  '  Given  by  inspiration  of  Grod. 
Joseph  Smith.'  A  leading  article  on  the  discoveries  of  Prof. 
Orson  Pratt  says,  'Mormonism  has  long  taken  the  lead  in  religion: 
it  will  soon  be  in  the  van  both  in  science  and  politics.'  At  the 
beginning  of  the  paper  is  Prof.  Pratt's  '  Law  of  Planetary  Rota- 
tion.' The  cube  roots  of  the  densities  of  the  planets  are  as  the 
square  roots  of  their  periods  of  rotation.  The  squares  of  the  cube 
roots  of  the  masses  divided  by  the  squares  of  the  diameters  are 
as  the  periods  of  rotation.  Arithmetical  verification  attempted, 
and  the  whole  very  modestly  stated  and  commented  on.  Dated 
Gr.  S.  L.  City,  Utah  Ter.,  Aug.  1,  1855.  If  the  creed,  as  above, 
be  correctly  given,  no  wonder  the  Mormonites  are  in  such  bad 
odour. 

The   two   estates ;    or  both   worlds    mathematically   considered. 
London,  1855,  small  (pp.  16). 

The  author  has  published  mathematical  works  with  his  name. 
The  present  tract  is  intended  to  illustrate  mathematically  a  point 
which  may  be  guessed  from  the  title.  But  the  symbols  do  very 
little  in  the  way  of  illustration  :  thus,  x  being  the  present  value 
of  the  future  estate  (eternal  happiness),  and  a  of  all  that  this 
world  can  give,  the  author  impresses  it  on  the  mathematician 
that,  x  being  infinitely  greater  than  a,  x  +  a—x,  so  that  a  need 
not  be  considered.  This  will  not  act  much  more  powerfully  on 
a  mathematician  by  virtue  of  the  symbols  than  if  those  same 
symbols  had  been  dispensed  with :  even  though,  as  the  author 
adds,  '  It  was  this  method  of  neglecting  infinitely  small  quantities 
that  Sir  Isaac  Newton  was  indebted  to  for  his  greatest  discoveries.' 

There  has  been  a  moderate  quantity  of  well-meant  attempt  to 
enforce,  sometimes  motive,  sometimes  doctrine,  by  arguments 
drawn  from  mathematics,  the  proponents  being  persons  unskilled 
in  that  science  for  the  most  part.  The  ground  is  very  dangerous : 
for  the  illustration  often  turns  the  other  way  with  greater  power, 
in  a  manner  which  requires  only  a  little  more  knowledge  to  see. 


MATHEMATICAL   ILLUSTRATIONS   OF   DOCTRINE.  295 

I  have,  in  my  life,  heard  from  the  pulpit  or  read,  at  least  a  dozen 
times,  that  all  sin  is  infinitely  great,  proved  as  follows.  The 
greater  the  being,  the  greater  the  sin  of  any  offence  against  him : 
therefore  the  offence  committed  against  an  infinite  being  is 
infinitely  great.  Now  the  mathematician,  of  which  the  proposers 
of  this  argument  are  not  aware,  is  perfectly  familiar  with 
quantities  which  increase  together,  and  never  cease  increasing, 
but  so  that  one  of  them  remains  finite  when  the  other  becomes 
infinite.  In  fact,  the  argument  is  a  perfect  non  sequitur.  Those 
who  propose  it  have  in  their  minds,  though  in  a  cloudy  and  in- 
definite form,  the  idea  of  the  increase  of  guilt  being  propor- 
tionate to  the  increase  of  greatness  in  the  being  offended.  But 
this  it  would  never  do  to  state  :  for  by  such  statement  not  only 
would  the  argument  lose  all  that  it  has  of  the  picturesque,  but 
the  asserted  premise  would  have  no  strong  air  of  exact  truth. 
How  could  any  one  undertake  to  appeal  to  conscience  to  declare 
that  an  offence  against  a  being  4-j-7^-  times  as  great  as  another  is 
exactly,  no  more  and  no  less,  4T7^-  times  as  great  an  offence  against 
the  other  ? 

The  infinite  character  of  the  offence  against  an  infinite  being 
is  laid  down  in  Dryden's  Religio  Laid,  and  is,  no  doubt,  an  old 
argument : — 

For,  granting  we  have  sinned,  and  that  th'  offence 

Of  man  is  made  against  Omnipotence, 

Some  price  that  bears  proportion  must  be  paid, 

And  infinite  with  infinite  be  weighed. 

See  then  the  Deist  lost ;  remorse  for  vice 

Not  paid  ;  or,  paid,  inadequate  in  price. 

Dryden,  in  the  words  '  bears  proportion '  is  in  verse  more 
accurate  than  most  of  the  recent  repeaters  in  prose,  And  this  is 
not  the  only  case  of  the  kind  in  his  argumentative  poetry. 

My  old  friend,  the  late  Dr.  Olinthus  Gregory,  who  was  a  sound 
and  learned  mathematician,  adopted  this  dangerous  kind  of 
illustration  in  his  Letters  on  the  Christian  Eeligion.  He  argued, 
by  parallel,  from  what  he  supposed  to  be  the  necessarily  mysterious 
nature  of  the  impossible  quantity  of  algebra  to  the  necessarily 
mysterious  nature  of  certain  doctrines  of  his  system  of  Chris- 
tianity. But  all  the  difficulty  and  mystery  of  the  impossible 
quantity  is  now  cleared  away  by  the  advance  of  algebraical 
thought :  and  yet  Dr.  Gregory's  book  continues  to  be  sold,  and 
no  doubt  the  illustration  is  still  accepted  as  appropriate. 

The  mode  of  argument  used  by  the  author  of  the  tract  above 


296  A  BUDGET   OF  PARADOXES. 

named  has  a  striking  defect.  He  talks  of  reducing  this  world 
and  the  next  to  '  present  value,'  as  an  actuary  does  with  succes- 
sive lives  or  next  presentations.  Does  value  make  interest  ?  and 
if  not,  why  ?  And  if  it  do,  then  the  present  value  of  an  eternity 
is  not  infinitely  great.  Who  is  ignorant  that  a  perpetual  annuity 
at  five  per  cent,  is  worth  only  twenty  years'  purchase  ?  This 
point  ought  to  be  discussed  by  a  person  who  treats  heaven  as  a 
deferred  perpetual  annuity.  I  do  not  ask  him  to  do  so,  and 
would  rather  he  did  not ;  but  if  he  will  do  it,  he  must  either 
deal  with  the  question  of  discount,  or  be  asked  the  reason  why. 

When  a  very  young  man,  I  was  frequently  exhorted  to  one  or 
another  view  of  religion  by  pastors  and  others  who  thought  that 
a  mathematical  argument  would  be  irresistible.  And  I  heard  the 
following  more  than  once,  and  have  since  seen  it  in  print,  I  forget 
where.  Since  eternal  happiness  belonged  to  the  particular  views 
in  question,  a  benefit  infinitely  great,  then,  even  if  the  probability 
of  their  arguments  were  small,  or  even  infinitely  small,  yet  the 
product  of  the  chance  and  benefit,  according  to  the  usual  rule, 
might  give  a  result  which  no  one  ought  in  prudence  to  pass  over. 
They  did  not  see  that  this  applied  to  all  systems  as  well  as  their 
own.  I  take  this  argument  to  be  the  most  perverse  of  all  the 
perversions  I  have  heard  or  read  on  the  subject :  there  is  some 
high  authority  for  it,  whom  I  forget. 

The  moral  of  all  this  is,  that  such  things  as  the  preceding 
should  be  kept  out  of  the  way  of  those  who  are  not  mathe- 
maticians, because  they  do  not  understand  the  argument ;  and  of 
those  who  are,  because  they  do. 

[The  high  authority  referred  to  above  is  Pascal,  an 
early  cultivator  of  mathematical  probability,  and  obviously  too 
much  enamoured  of  his  new  pursuit.  But  he  conceives  himself 
bound  to  wager  on  one  side  or  the  other.  To  the  argument 
(Pensees,  ch.  7)  that  '  le  juste  est  de  ne  point  parier,'  he  answers, 
'  Oui :  mais  il  faut  parier :  vous  6tes  embarque ;  et  ne  parier 
point  que  Dieu  est,  c'est  parier  qu'il  n'est  pas.'  Leaving  Pascal's 
argument  to  make  its  way  with  a  person  who,  being  a  sceptic,  is 
yet  positive  that  the  issue  is  salvation  or  perdition,  if  a  Grod  there 
be, — for  the  case  as  put  by  Pascal  requires  this, — I  shall  merely 
observe  that  a  person  who  elects  to  believe  in  Grod,  as  the  best 
chance  of  gain,  is  not  one  who,  according  to  Pascal's  creed,  or 
any  other  worth  naming,  will  really  secure  that  gain;  I  wonder 
whether  Pascal's  curious  imagination  ever  presented  to  him  in 
sleep  his  convert,  in  the  future  state,  shaken  out  of  a  red-hot 
dice-box  upon  a  red-hot  hazard»table,  as  perhaps  he  might  have 


XOVUM  OBGANOI  MORALIUM.  297 

been,  if  Dante  had  been  the  later  of  the  two.  The  original  idea 
is  due  to  the  elder  Arnobius,  who,  as  cited  by  Bayle,  speaks 
thus: — 

'  Sed  et  ipse  [Christus]  quse  pollicetur,  non  probat.  Ita  est.  Xulla 
enim,  ut  dixi,  futnrorum  potest  existere  comprobatio.  Cum  ergo  haec 
sit  conditio  rntnroruni,  ut  teneri  et  comprehend!  nnllius  possint 
anticipationis  attactu  ;  nonne  purior  ratio  est,  ex  duobus  incertis,  et  in 
ambigua  expectatione  pendentibus,  id  potius  credere,  quod  aliqnas 
spes  ferat,  quam  omnino  quod  nnllas  ?  In  illo  enim  periculi  nihil  est, 
si  quod  dicitur  imminere,  cassnm  fiat  et  vacuum  :  in  hoc  damnum 
est  maximum,  id  est  salutis  amissio,  si  cum  tempus  advenerit  aperiatur 
non  faisse  mendacium.' 

Really  Arnobius  seems  to  have  got  as  much  out  of  the  notion, 
in  the  third  century,  as  if  he  had  been  fourteen  centuries  later, 
with  the  arithmetic  of  chances  to  help  him.] 

The  Sentinel,  vol.  ix.  no.  27.     London,  Saturday,  May  26,  1855. 

This  is  the  first  London  number  of  an  Irish  paper,  Protestant 
in  politics.  It  opens  with  '  Suggestions  on  the  subject  of  a  3*t"-</  m 
Organum  Moralium^  which  is  the  application  of  algebra  and  the 
differential  calculus  to  morals,  socials,  and  politics.  There  is  also  a 
leading  article  on  the  subject,  and  some  applications  in  notes  to 
other  articles.  A  separate  publication  was  afterwards  made,  with 
the  addition  of  a  long  Preface  ;  the  author  being  a  clergyman  who 
I  presume  must  have  been  the  editor  of  the  Sentinel. 

Suggestions  as  to  the  employment  of  a  Novum  Organum  Mora- 
Hum.  Or,  thoughts  on  the  nature  of  the  Differential  Calculus, 
and  on  the  application  of  its  principles  to  metaphysics,  with  a 
view  to  the  attainment  of  demonstration  and  certainty  in  moral, 
political  and  ecclesiastical  affairs.  By  Tresham  Dames  Gregg, 
Chaplain  of  St.  Mary's,  within  the  church  of  St.  Nicholas  intra 
mnros,  Dublin.  London  1859,  8vo.  (pp.  xl  +  32). 

I  have  a  personal  interest  in  this  system,  as  will  appear  from 
the  following  extract  from  the  newspaper  : — 

'  "We  were  subsequently  referred  to  De  Morgan's  "  Formal  Logic  " 
and  Boole's  "  Laws  of  Thought,"  both  very  elaborate  works,  and 
greatly  in  the  direction  taken  by  ourselves.  That  the  writers  amazingly 
surpass  us  in  learning  we  most  willingly  admit,  but  we  venture  to 
pronounce  of  both  their  learned  treatises,  that  they  deal  with  the 
subject  in  a  mode  that  is  scholastic  to  an  excess  .  .  .  That  their  works 
have  been  for  a  considerable  space  of  time  before  the  world  and 


298  A  BUDGET  OF  PARADOXES. 

effected  nothing,  would  argue  that  they  have  overlooked  the  vital 
nature  of  the  theme.  .  .  On  the  whole,  the  writings  of  De  Morgan  and 
Boole  go  to  the  full  justification  of  our  principle  without  in  any  wise 
so  trenching  upon  our  ground  as  to  render  us  open  to  reproach  in 
claiming  our  Calculus  as  a  great  discovery.  .  .  But  we  renounce  any 
paltry  jealousy  as  to  a  matter  so  vast.  If  De  Morgan  and  Boole  have 
had  a  priority  in  the  case,  to  them  we  cheerfully  shall  resign  the  glory 
and  honour.  If  such  be  the  truth,  they  have  neither  done  justice  to 
the  discovery,  nor  to  themselves  [quite  true].  They  have,  under  the 
circumstances,  acted  like  '  the  foolish  man,  who  roasteth  not  that 
which  he  taketh  in  hunting.'  .  .  It  will  be  sufficient  for  us,  however,  to 
be  the  Columbus  of  these  great  Americi,  and  popularise  what  they 
found,  if  they  found  it.  We,  as  from  the  mountain  top,  will  then 
become  their  trumpeters,  and  cry  glory  to  De  Morgan  and  glory  to 
Boole,  under  Him  who  is  the  source  of  all  glory,  the  only  good  and 
wise,  to  Whom  be  glory  for  ever !  If  they  be  our  predecessors  in 
this  matter,  they  have,  under  Him,  taken  moral  questions  out  of  the 
category  of  probabilities,  and  rendered  them  perfectly  certain.  In  that 
case,  let  their  books  be  read  by  those  who  may  doubt  the  principles  this 
day  laid  before  the  world  as  a  great  discovery,  by  our  newspaper. 
Our  cry  shall  be  tvprjKaai  \  Let  us  hope  that  they  will  join  us,  and 
henceforth  keep  their  right  [sic]  from  under  their  bushel.' 

For  myself,  and  for  my  old  friend  Mr.  Boole,  who  I  am  sure 
would  join  me,  I  disclaim  both  priority,  simultaneity,  and 
posteriority,  and  request  that  nothing  may  be  trumpeted  from 
the  mountain  top  except  our  abjuration  of  all  community  of 
thought  or  operation  with  this  Novum  Organum. 

To  such  community  we  can  make  no  more  claim  than  Americus 
could  make  to  being  the  forerunner  of  Columbus  who  popularised 
his  discoveries.  We  do  not  wish  for  any  svprjicao-i,  and  not  even  for 
svprjKaa-i.  For  self  and  Boole,  I  point  out  what  would  have  con- 
vinced either  of  us  that  this  house  is  divided  against  itself. 
.  A  being  the  apostolic  element,  8  the  doctrinal  element,  and 
X  the  body  of  the  faithful,  the  church  is  A  8  X,  we  are  told. 
Also,  that  if  A  become  negative,  or  the  Apostolicity  become 
Diabolicity  [my  words] ;  or  if  8  become  negative,  and  doctrine 
become  heresy ;  or  if  X  become  negative,  that  is,  if  the  faithful 
become  unfaithful ;  the  church  becomes  negative,  *  the  very 
opposite  of  what  it  ought  to  be.'  For  self  and  Boole,  I  admit 
this.  But — which  is  not  noticed — if  A  and  8  should  both  become 
negative,  diabolical  origin  and  heretical  doctrine,  then  the  church, 
A  8  X,  is  still  positive,  what  it  ought  to  be,  unless  X  be  also 
negative,  or  the  people  unfaithful  to  it,  in  which  case  it  is  a  bad 
church.  Now,  self  and  Boole — though  I  admit  I  have  not  asked 


DE  MORGAN  AND  BOOLE  CORRECTED.  299 

my  partner — are  of  opinion  that  a  diabolical  church  with  falsfe 
doctrine  does  harm  when  the  people  are  faithful,  and  can  do 
good  only  when  the  people  are  unfaithful.  We  may  be  wrong^ 
but  this  is  what  we  do  think.  Accordingly,  we  have  caught 
nothing,  and  can  therefore  roast  nothing  of  our  own :  I  content 
myself  with  roasting  a  joint  of  Mr.  Gregg's  larder. 

These  mathematical  vagaries  have  uses  which  will  justify  a 
large  amount  of  quotation :  and  in  a  score  of  years  this  may 
perhaps  be  the  only  attainable  record.  I  therefore  proceed. 

After  observing  that  by  this  calculus  juries  (heaven  help  them  I 
say  I)  can  calculate  damages  '  almost  to  a  nicety,'  and  further 
that  it  is  made  abundantly  evident  that  c  e  x  is  '  the  general 
expression  for  an  individual,'  it  is  noted  that  the  number  of  the 
Beast  is  not  given  in  the  Revelation  in  words  at  length,  but  as 
X&  •  On  this  the  following  remark  is  made  : — 

'  Can  it  be  possible  that  we  have  in  this  case  a  specimen  given  to  us 
of  the  arithmetic  of  heaven,  and  an  expression  revealed,  which  indicates 
by  its  function  of  addibility,  the  name  of  the  church  in  question,  and 
of  each  member  of  it ;  and  by  its  function  of  multiplicability  the 
doctrine,  the  mission,  and  the  members  of  the  great  Synagogue  of 
Apostacy  ?  We  merely  propound  these  questions  ; — we  do  not  pretend 
to  solve  them.' 

After  a  translation  in  blank  verse  —a  very  pretty  one-  -of  the 
18th  Psalm,  the  author  proceeds  as  follows,  to  render  it  into 
differential  calculus : — 

'  And  the  whole  tells  us  just  this,  that  David  did  what  he  could.  He 
augmented  those  elements  of  his  constitution  which  were  (exceptis 
excipiendis)  subject  to  himself,  and  the  Almighty  then  augmented  his 
personal  qualities,  and  his  vocational  status.  Otherwise,  to  throw  the 
matter  into  the  expression  of  our  notation,  the  variable  e  was  aug- 
mented, and  c  x  rose  proportionally.  The  law  of  the  variation,  accord- 
ing to  our  theory,  would  be  thus  expressed.  The  resultant  was  David 
the  king  c  e  x  [c=r?]  (who  had  been  David  the  shepherd  boy),  and 
from  the  conditions  of  the  theorem  we  have 

- du  dx   .          dc 

_   =  c  e  - — \-ex-      x  +  c  x 
de  de  de 

which,  in  the  terms  of  ordinary  language,  just  means,  the  increase  of 
David's  educational  excellence  or  qualities — his  piety,  his  prayerfulness, 
his  humility,  obedience,  &c. — was  so  great,  that  when  multiplied  by  his 
original  talent  and  position,  it  produced  a  product  so  great  as  to  be 
equal  in  its  amount  to  royalty,  honour,  wealth,  and  power,  &c.  :  in 
short,  to  all  the  attributes  of  majesty.' 

The  '  solution  of  the  family  problem '  is  of  high  interest.     It  is 


300  A  BUDGET  OF  PARADOXES. 

to  determine  the  effect  on  the  family  in  general  from  a  change 
[of  conduct]  in  one  of  them.  The  person  chosen  is  one  of  the 
maid-servants. 

'  Let  c  e  a  be  the  father ;  CiC]Xl  the  mother,  &c.  The  family  then 
consists  of  the  maid's  master,  her  mistress,  her  young  master,  her 
young  mistress,  and  fellow  servant.  Now  the  master's  calling  (or  c) 
is  to  exercise  his  share  of  control  over  this  servant,  and  mind  the  rest 
of  his  business  :  call  this  remainder  a,  and  let  his  calling  generally,  or 

all  his  affairs,  be  to  his  maid-servant  as  m  :  y,  i.  e.,  y  =        ; .  .  .  .  and 

c 

this  expression  will  represent  his  relation  to  the  servant.    Consequently, 

(i    mz\  ,-,         .       /      ,     mz\ 

a  +  -      }  e  x ;  otherwise  (  a  +  —   ]  e  x 
c  )  \  c  / 

is  the  expression  for  the  father  when  viewed  as  the  girl's  master.' 

I  have  no  objection  to  repeat  so  far;  but  I  will  not  give  the 
formula  for  the  maid's  relation  to  her  young  master ;  for  I  am 
not  quite  sure  that  all  young  masters  are  to  be  trusted  with  it. 
Suffice  it  that  the  son  will  be  affected  directly  as  his  influence 
over  her,  and  inversely  as  his  vocational  power  :  if  then  he  should 
have  some  influence  and  no  vocational  power,  the  effect  on  him 
would  be  infinite.  This  is  dismal  to  think  of.  Further,  the 
formula  brings  out  that  if  one  servant  improve,  the  other  must 
deteriorate,  and  vice  versa.  This  is  not  the  experience  of  most 
families  :  and  the  author  remarks  as  follows : — 

'  That  is,  we  should  venture  to  say,  a  very  beautiful  result,  and  we 
may  say  it  yielded  us  no  little  astonishment.  What  our  calculation 
might  lead  to  we  never  dreamt  of ;  that  it  should  educe  a  conclusion 
so  recondite  that  our  unassisted  power  never  could  have  attained  to, 
and  which,  if  we  could  have  conjectured  it,  would  have  been  at  best 
the  most  distant  probability,  that  conclusion  being  itself,  as  it  would 
appear,  the  quintessence  of  truth,  afforded  us  a  measure  of  satisfaction 
that  was  not  slight.' 

That  the  writings  of  Mr.  Boole  and  myself  '  go  to  the  full 
justification  of  this  '  principle,'  is  only  true  in  the  sense  in  which 
the  Scotch  use,  or  did  use,  the  word  justification. 

[The  last  number  of  this  Budget  had  stood  in  type  for  months, 
waiting  until  there  should  be  a  little  cessation  of  correspondence 
more  connected  with  the  things  of  the  day.  I  had  quite  for- 
gotten what  it  was  to  contain ;  and  little  thought,  when  I  read 
the  proof,  that  my  allusions  to  my  friend  Mr.  Boole,  then  in  life 
and  health,  would  not  be  printed  till  many  weeks  after  his  death. 
Had  I  remembered  what  my  last  number  contained,  I  should  have 


BOOLE'S  LAWS   OF  THOUGHT.  301 

added  my  expression  of  regret  and  admiration  to  the  numerous 
obituary  testimonials,  which  this  great  loss  to  science  has  called 
forth. 

The  system  of  logic  alluded  to  in  the  last  number  of  this  series 
is  but  one  of  many  proofs  of  genius  and  patience  combined.  I 
might  legitimately  have  entered  it  among  my  paradoxes,  or 
things  counter  to  general  opinion  :  but  it  is  a  paradox  which,  like 
that  of  Copernicus,  excited  admiration  from  its  first  appearance. 
That  the  symbolic  processes  of  algebra,  invented  as  tools  of 
numerical  calculation,  should  be  competent  to  express  every  act 
of  thought,  and  to  furnish  the  grammar  and  dictionary  of  an  all- 
containing  system  of  logic,  would  not  have  been  believed  until  it 
was  proved.  When  Hobbes,  in  the  time  of  the  Commonwealth, 
published  his  '  Computation  or  Logique,'  he  had  a  remote  glimpse 
of  some  of  the  points  which  are  placed  in  the  light  of  day  by  Mr. 
Boole.  The  unity  of  the  forms  of  thought  in  all  the  applications 
of  reason,  however  remotely  separated,  will  one  day  be  matter 
of  notoriety  and  common  wonder  :  and  Boole's  name  will  be  re- 
membered in  connexion  with  one  of  the  most  important  steps 
towards  the  attainment  of  this  knowledge.] 

The  Decimal  System  as  a  whole.    By  Dover  Statter.    London  and 

Liverpool,  1856,  8vo. 

The  proposition  is  to  make  everything  decimal.  The  day,  now 
24  hours,  is  to  be  made  10  hours.  The  year  is  to  have  ten  months, 
Unusber,  Duober,  &c.  Fortunately  there  are  ten  commandments, 
so  there  will  be  neither  addition  to,  nor  deduction  from,  the 
moral  law.  But  the  twelve  apostles  I  Even  rej  ecting  Judas, 
there  is  a  whole  apostle  of  difficulty.  These  points  the  author 
does  not  touch. 

The  first  book  of  Phonetic  Reading.  London,  Fred.  Pitman, 
Phonetic  Depot,  20,  Paternoster  Bow,  1856,  12mo. 

The  Phonetic  Journal.  Devoted  to  the  propagation  of  phonetic 
reading,  phonetic .  longh and,  phonetic  shorthand,  and  phonetic 
printing.  No.  46.  Saturday,  15  November  1856.  Vol.  15. 

I  write  the  titles  of  a  couple  out  of  several  tracts  which  I 
have  by  me.  But  the  number  of  publications  issued  by  the  pro- 
moters of  this  spirited  attempt  is  very  large  indeed.  The  attempt 
itself  has  had  no  success  with  the  mass  of  the  public.  This  I  do 
not  regret.  Had- the  world  found  that  the  change  was  useful,  I 
should  have  gone  contentedly  with  the  stream  ;  but  not  without 
regretting  our  old  language.  I  admit  the  difficulties  which  our 


302  A  BUDGET  OF  PAKADOXES. 

unpronouncable  spelling  puts  in  the  way  of  learning  to  read :  and 
I  have  no  doubt  that,  as  affirmed,  it  is  easier  to  teach  children 
phonetically,  and  afterwards  to  introduce  them  to  our  common 
system,  than  to  proceed  in  the  usual  way.  But  by  the  usual  way 
I  mean  proceeding  by  letters  from  the  very  beginning.  If,  which 
I  am  sure  is  a  better  plan,  children  be  taught  at  the  commence- 
ment very  much  by  complete  words,  as  if  they  were  learning 
Chinese,  and  be  gradually  accustomed  to  resolve  the  known  words 
into  letters,  a  fraction,  perhaps  a  considerable  one,  of  the  advan- 
tage of  the  phonetic  system  is  destroyed.  It  must  be  remem- 
bered that  a  phonetic  system  can  only  be  an  approximation.  The 
differences  of  pronunciation  existing  among  educated  persons 
are  so  great,  that,  on  the  phonetic  system,  different  persons  ought 
to  spell  differently. 

But  the  phonetic  party  have  produced  something  which  will 
immortalize  their  plan  :  I  mean  their  shorthand,  which  has  had 
a  fraction  of  the  success  it  deserves.  All  who  know  anything  of 
shorthand  must  see  that  nothing  but  a  phonetic  system  can  be 
worthy  of  the  name  :  and  the  system  promulgated  is  skilfully 
done.  Were  I  a  young  man  I  should  apply  myself  to  it  syste- 
matically. I  believe  this  is  the  only  system  in  which  books  were 
ever  published.  I  wish  some  one  would  contribute  to  a  public 
journal  a  brief  account  of  the  dates  and  circumstances  of  the 
phonetic  movement,  not  forgetting  a  list  of  the  books  published 
in  shorthand. 

A  child  beginning  to  read  by  himself  may  owe  terrible  dreams 
and  waking  images  of  horror  to  our  spelling,  as  I  did  when  six 
years  old.  In  one  of  the  common  poetry-books  there  is  an  ad- 
monition against  confining  little  birds  in  cages,  and  the  child  is 
asked  what  if  a  great  giant,  amazingly  strong,  were  to  take  you 
away,  shut  you  up, 

And  feed  you  with  vic-tu-als  you  ne-ver  could  bear. 

The  book  was  hyphened  for  the  beginner's  use ;  and  I  had  not  the 
least  idea  that  vic-tu-als  were  vittles :  by  the  sound  of  the  word 
I  judged  they  must  be  of  iron ;  and  it  entered  into  my  soul. 

The  worst  of  the  phonetic  shorthand  books  is  that  they  nowhere, 
so  far  as  I  have  seen,  give  all  the  symbols,  in  every  stage  of  ad- 
vancement, together,  in  one  or  following  pages.  It  is  symbols 
and  talk,  more  symbols  and  more  talk,  &c.  A  universal  view  of 
the  signs  ought  to  begin  the  works. 


MAGNITUDE   OF   THE   EARTH— THE   MOON.  303 


Ombrological  Almanac.  Seventeenth  year.  An  essay  on  Anemo- 
logy  and  Ombrology.  By  Peter  Legh,  Esq.  London,  1856, 
12mo. 

Mr.  Legh,  already  mentioned,  was  an  intelligent  country 
gentleman,  and  a  legitimate  speculator.  But  the  clue  was  not 
reserved  for  him. 


The  proof  that  the  three  angles  of  a  triangle  are  equal  to  two 
right  angles  looked  for  in  the  inflation  of  the  circle.  By  Gen. 
Perronet  Thompson.  London,  1856,  8vo.  (pp.  4.) 

Another  attempt,  the  third,  at  this  old  difficulty,  which  cannot 
be  put  into  few  words  of  explanation. 

Comets  considered  as  volcanoes,  and  the  cause  of  their  velocity 
and  other  phenomena  thereby  explained.  London  (circa  1856), 
8vo. 

The  title  explains  the  book  better  than  the  book  explains  the 
title. 

1856.  A  stranger  applied  to  me  to  know  what  the  ideas 
of  a  friend  of  his  were  worth  upon  the  magnitude  of  the  earth. 
The  matter  being  one  involving  points  of  antiquity,  I  mentioned 
various  persons  whose  speculations  he  seemed  to  have  ignored ; 
among  others,  Thales.  The  reply  was,  '  I  am  instructed  by  the 
author  to  inform  you  that  he  is  perfectly  acquainted  with  the 
works  of  Thales,  Euclid,  Archimedes,  .  .  .  '  I  had  some  thought 
of  asking  whether  he  had  used  the  Elzevir  edition  of  Thales, 
which  is  known  to  be  very  incomplete,  or  that  of  Prof.  Niemand 
with  the  lections,  Nirgend,  1824,  2  vols.  folio  ;  just  to  see  whether 
the  last  would  not  have  been  the  very  edition  he  had  read.  But 
I  refrained,  in  mercy. 

The  moon  is  the  image  of  the  Earth,  and  is  not  a  solid  body.  By 
The  Longitude.  (Private  Circulation.)  In  five  parts.  London, 
1856,  1857,  1857 ;  Calcutta,  1858,  1858,  8vo. 

The  earth  is  *  brought  to  a  focus ' ;  it  describes  a  *  looped ' 
orbit  round  the  sun.  The  eclipse  of  the  sun  is  thus  explained  : 
'  At  the  time  of  eclipses,  the  image  is  more  or  less  so  directly 
before  or  behind  the  earth  that,  in  the  case  of  new  moon,  bright 
rays  of  the  sun  fall  and  bear  upon  the  spot  where  the  figure  of 
the  earth  is  brought  to  a  focus,  that  is,  bear  upon  the  image  of 


304  A  BUDGET  OF  PARADOXES. 

the  earth,  when  a  darkness  beyond  is  produced  reaching  to  the 
earth,  and  the  sun  becomes  more  or  less  eclipsed.'  How  the 
earth  is  '  brought  to  a  focus '  we  do  not  find  stated.  Writers  of 
this  kind  always  have  the  argument  that  some  things  which  have 
been  ridiculed  at  first  have  been  finally  established.  Those  who 
put  into  the  lottery  had  the  same  kind  of  argument  ;  but  were 
always  answered  by  being  reminded  how  many  blanks  there  were 
to  one  prize.  I  am  loath  to  pronounce  against  anything :  but  it 
does  force  itself  upon  me  that  the  author  of  these  tracts  has 
drawn  a  blank. 

Times,  April  6  or  7,  1856.     The  moon  has  no  rotary  motion. 

A  letter  from  Mr.  Jellinger  Symons,  inspector  of  schools,  which 
commenced  a  controversy  of  many  letters  and  pamphlets.  This 
dispute  comes  on  at  intervals,  and  will  continue  to  do  so.  It 
sometimes  arises  from  inability  to  understand  the  character  of 
simple  rotation,  geometrically;  sometimes  from  not  understanding 
the  mechanical  doctrine  of  rotation. 

Lunar  Motion.  The  whole  argument  stated,  and  illustrated  by 
diagrams ;  with  letters  from  the  Astronomer  Royal.  By 
Jellinger  C.  Symons.  London,  185(3,  8vo. 

The  Astronomer  Koyal  endeavoured  to  disentangle  Mr.  J.  C. 
Symons,  but  failed.  Mr.  Airy  can  correct  the  error  of  a  ship's 
compasses,  because  he  can  put  her  head  which  way  he  pleases  : 
but  this  he  cannot  do  with  a  speculator. 

Mr.  Symons,  in  this  tract,  insinuated  that  the  rotation  of  the 
moon  is  one  of  the  silver  shrines  of  the  craftsmen.  To  see  a 
thing  so  clearly  as  to  be  satisfied  that  all  who  say  they  do  not  see 
it  are  telling  wilful  falsehood,  is  the  nature  of  man.  Many  of  all 
sects  find  much  comfort  in  it,  when  they  think  of  the  others ; 
many